CHAPTER 3 ENERGY EFFICIENT DESIGN OF INDUCTION MOTOR USNG GA

Transcription

1 31 CHAPTER 3 ENERGY EFFICIENT DESIGN OF INDUCTION MOTOR USNG GA 3.1 INTRODUCTION Electric motors consume over half of the electrical energy produced by power stations, almost the three-quarters of the electrical consumption in industry and almost the half of commercial electrical consumption in developed countries. Hence, motors constitute the main targets to achieve energy saving. Owing to their simple and robust construction, the asynchronous motors represent about 90-95% of the electrical energy consumption of electric motors, which is equivalent to about 53% of total electrical energy consumption. Hence, it is much desired by both manufacturer and the user to optimize the design for improving the energy efficiency and reducing the cost of active materials (iron and copper) of the motor. The energy efficiency of a motor can be optimized by reducing the weight of active materials used, which can be achieved by reducing the diameter and length of the motor. 3.2 OPTIMIZATION TECHNIQUES Optimization is a mathematical discipline that concerns the finding of minima and maxima of functions, subject to so-called constraints. Optimization originated in the 1940s, when George Dantzig used mathematical techniques for generating "programs" (training timetables and

2 32 schedules) for military application. Since then, his "linear programming" techniques and their descendents were applied to a wide variety of problems. Today, optimization comprises a wide variety of techniques from Operations Research, Artificial Intelligence and Computer Science which are used to improve business processes practically in all industries. Over the past decade, a number of optimization techniques have been studied and developed. The Evolutionary computation community has shown a significant interest in optimization for many years. In particular, there has been a focus on global optimization of numerical, real- valued problems for which exact and analytical methods do not apply. Since, many general-purpose optimization algorithms have been proposed for finding optimal solutions; notably: Evolution Strategies, Evolutionary Programming, Genetic algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). Many efforts have been devoted to compare these algorithms to one another. Typically, such comparisons have been based on artificial numerical benchmark problems. However, in certain situations of practical interest, it is often necessary to obtain the global optimal solution rather than the local optimal solution. Broadly the global optimization techniques may be divided into stochastic and deterministic search techniques. The deterministic techniques depend on the mathematical nature (like differentiability, continuity etc.) of the problem whereas the stochastic techniques are considered to be more user friendly because they do not depend on the mathematical properties of a given function and are hence more appropriate for finding the global optimal solutions for any type of objective function. Genetic algorithm is one such method of stochastic technique of optimization which is found to be the most effective and superior amongst all. Also, the initial attempts with different starting points need not be close to actual values. Another advantage is that it

3 33 does not require the use of the derivative of the function, which is not always easily obtainable or may not even exist, for example, when dealing with real measurements involving noisy data. Hence, in the present study, Genetic Algorithm (GA) is used as the optimization tool for energy efficient design of induction motor. 3.3 GENETIC ALGORITHM The GA is a method for solving both constrained and unconstrained optimization problems that is based on natural selection, the process that drives biological evolution. The GA repeatedly modifies a population of individual solutions. At each step, it selects individuals at random from the current population to be parents and uses them to produce the children for the next generation. Over successive generations, the population "evolves" toward an optimal solution. GA can also be used for solving a variety of optimization problems that are not well suited for standard optimization algorithms, including problems in which the objective function is discontinuous, not differentiable, stochastic, or highly nonlinear. The GA uses three main types of rules at each step to create the next generation from the current population: Selection rules select the individuals, called parents that contribute to the population at the next generation. Crossover rules combine two parents to form children for the next generation. Mutation rules apply random changes to individual parents to form children.

4 34 works: The following outline summarizes how the genetic algorithm 1. The algorithm begins by creating a random initial population. 2. The algorithm then creates a sequence of new populations. At each step, the algorithm uses the individuals in the current generation to create the next population by performing the following steps: a. Scores each member of the current population by computing its fitness value. b. Scales the raw fitness scores to convert them into a more usable range of values. c. Selects members, called parents, based on their fitness. d. Some of the individuals in the current population that have lower fitness are chosen as elite. These elite individuals are passed to the next population. e. Produces children from the parents. Children are produced either by making random changes to a single parent (mutation) or by combining the vector entries of a pair of parents (crossover). f. Replaces the current population with the children to form the next generation. 3. The algorithm stops when one of the stopping criterion is met.

5 CONCEPT OF ENERGY EFFICIENCY Since, induction motor is treated as a generalized transformer; efficiency of the motor can be expressed both in terms of power and energy. Accordingly, they are termed as commercial efficiency and energy efficiency. Commercial efficiency is calculated for a load at a particular instant. Energy efficiency is calculated for a day. The efficiency of a motor is determined by intrinsic losses that can be reduced only by changes in motor design. Intrinsic losses are of two types: fixed losses - independent of motor load, and variable losses - dependent on load. Energy-efficient motors (EEM) are the ones in which, design improvements are incorporated specifically to increase operating efficiency over motors of standard design. Design improvements focus on reducing intrinsic motor losses. Improvements include the use of lower-loss silicon steel, a longer core (to increase active material), thicker wires (to reduce resistance), thinner laminations, smaller air gap between stator and rotor, copper instead of aluminum bars in the rotor, superior bearings and a smaller fan, etc. In keeping with the stipulations of the Beauro of Indian Standards (BIS), energy-efficient motors should be designed to operate without loss in efficiency at loads between 75 % and 100 % of rated capacity. This may result in major benefits in varying load applications. The power factor is about the same or may be higher than for standard motors. Furthermore, energy- efficient motors have lower operating temperatures and noise levels, greater ability to accelerate higher-inertia loads, and are less affected by supply voltage fluctuations. 3.5 INDUCTION MOTOR DESIGN EQUATIONS The design Equations of an induction motor are derived from the output Equation of the machine. Since, output of induction motor is mechanical energy; its electrical equivalent in kva at the input is considered for deriving the design Equations. For converting the output power in HP to

6 36 input power in kva, values of expected efficiency and power factor will have to be assumed. The kva input is calculated from HP output using the relation given in Equation (3.1). kva input, S= (3.1) Output Equation Output Equation of an induction machine is the relation between the rated electrical power handling capacity of the machine and the main dimensions, namely diameter (D) and length (L) of the machine. The power output of an induction motor being mechanical in nature, the electrical power handling capacity is considered as the rated input for an assumed efficiency and power factor. The output Equation is derived from the basic Equation for the kva input to the motor as given in Equation (3.2). kva input, S = 3E ph I ph x 10-3 (3.2) where E ph and I ph are the per phase voltage and current of the induction motor. The above Equation is modified by replacing E ph with emf equation such that the main dimensions of the machine, the diameter and the length are introduced in to the Equation (3.2) as given in Equation (3.3) The modified equation is S = (1.1 2 B av ac k w x 10 _3 ) D 2 L n s kva (3.3) where, B av is termed as specific magnetic loading, ac is termed as specific electric loading and n s is the synchronous speed in rps.

7 37 Specific magnetic loading, B av, denoted as x 5 and the specific electric loading ac, denoted as x 1 in the present work are calculated as follows. x 5 = ; x 1 = The values of x 1 and x 5 are assumed for the given application. Therefore, the term given within in the bracket of Equation (3.3) is a constant and is named as output coefficient, C 0. Hence, output Equation is modified as given in Equation (3.4) S = C 0 D 2 Ln s kva. (3.4) Equations for Calculation of Iron Loss When the ferromagnetic materials are subjected to magnetization in a fixed direction in space and having a magnitude varying in time, losses are produced in the material. These losses are called iron losses or core losses. The core of the AC machine that carries the alternating flux is subject to iron losses. The total iron loss in the machine is the sum of stator iron loss and the rotor iron loss. Since, the frequency in the rotor is slip frequency which is not more than 2Hz, the iron losses in rotor side is assumed to be negligible for all practical purposes. Stator Iron Loss (SIL) is calculated using the Equation (3.5) SIL = (W t W tk +W c W ck )watts. (3.5) where, W iron loss constant for stator teeth (W/kg) and W iron loss constant for stator core (W/kg) The weight of the stator teeth (W t ) and stator core (W c ) are calculated using the Equations (3.6) and (3.7)

8 38 W t = is 1 d ss t s L i 10 6 kg (3.6) W = kg (3.7) where i is the density of iron, S 1 is the number of stator slots and x 4 is the stator core depth in mm. L i, the length of iron in core is calculated using Equation (3.8) L i = k i (L-0.001n d w d ) (3.8) where n d is the number ventilating ducts and w d is the width of a duct. Equation (3.9) The mean value of stator tooth width, t s is calculated using t s = (D+0.001d ss) S d ss x 3 m (3.9) where x 3 is the ratio of stator slot depth to width. The depth of stator slot, d ss, is calculated using the Equation (3.10) d = mm (3.10) where x 2 is the ratio length to pole pitch, x 6 is stator winding current density, Y is the pole pitch and S f is slot fullness factor. The outer diameter, OD, is calculated as given in Equation (3.11) OD = (D d ss x 4 ) m (3.11)

9 Equations for Calculation of Copper Loss Copper losses taking place in both stator and rotor is the main energy loss taking place in the machine. The copper loss taking place in stator (SCL) is calculated as given in Equation (3.12) SCL = 3I R (3.12) Equation (3.13) R s, the stator resistance per phase is calculated using R s = c E ph x K w fi ph Yx 5 + ( x x 2 Y ) (3.13) Rotor copper loss (RCL) is calculated using Equation (3.14) RCL = r S 2I b 2 a b (L r + 2D e p ) (3.14) density. S 2 represents the number of rotor slots and x 7 is the rotor current Rotor bar current I b is calculated using Equation (3.15) I b = 850Q 2.22K w fy 2 S 2 x 2 x 5 (3.15) The area of rotor bar, a b is calculated using Equation (3.16) a b = S K w fy 2 S 2 x 2 x 5 x 7 (3.16) Length of rotor bar, L r = L The diameter of end ring D e is calculated using Equation (3.17)

10 40 D e = D-0.002l g d sr (3.17) where l g is the radial air gap length and d sr is the depth of rotor slots. The value of d sr is calculated using Equation (3.18) d sr = a srs 2 x 3 S 1 d ss (3.18) The rotor slot area, a sr, is calculated using Equation (3.19) a sr = a b s fr (3.19) S fr is rotor slot fullness factor =1 for cast iron. A summary of energy efficiency improvements in induction machines is given in the Table 3.1. Table 3.1 Various means of efficiency improvements Type of power loss Iron Stator I 2 R losses Rotor I 2 R losses Friction and Windage losses Stray Load losses Efficiency improvements Use of thinner gauge, lower loss core steel reduces eddy current losses. Longer core adds more steel to the design, which reduces losses due to lower operating flux densities. Use of more copper and larger conductors increases cross sectional area of stator windings. This lowers resistance (R) of the windings and reduces losses due to current flow (I). Use of larger rotor conductor bars increases size of cross section, lowering conductor resistance (R) and losses due to current flow (I) Use of low loss fan design reduces losses due to air movement Use of optimized design and strict quality control procedures minimizes stray losses

11 ENERGY EFFICIENT DESIGN USING GA For optimizing the energy efficiency of the motor, various losses taking place in the motor should be minimized. Major losses taking place in the motor are fixed losses which are independent of motor load and variable losses which depend on load. Fixed losses consist of iron losses, friction and windage losses. Iron losses consist of eddy current and hysteresis losses in the stator. They vary with the core material, geometry and with input voltage. Friction and windage losses are caused by friction in the bearings of the motor and aerodynamic losses associated with the ventilation fan and other rotating parts. Variable losses consist of resistance losses in the stator and in the rotor and miscellaneous stray losses. Stray load losses arise from a variety of sources and are difficult to either measure directly or to calculate, but are generally proportional to the square of the rotor current. Stray load losses are taken as 1.8% of total losses for machines of rating 1-125HP. The design optimization program takes into account the Equations (3.1) to (3.19) and yield an optimized version of design of an induction motor. This program optimizes an already available design for a specified power rating to give best efficiency. The program is written using MATLAB. The optimization problem for the proposed three phase induction motor design is formulated as given in Equation (3.20) Minimize F(X) = 1/ (3.20) where F(X) is the objective function, X is the design variable set and is the efficiency of the motor. There are many variables in the design of an

12 42 induction motor and it is very difficult to accommodate all the variables in the optimization process. In the present work, seven independent design variables are selected as constraints. Hence, X is a set of seven variables as given in Equation (3.21). The design variables of the proposed work along with their limiting values are given in Table 3.2 X= {x 1, x 2, x 3, x 4, x 5, x 6, x 7 } (3.21) Table 3.2 Design variables along with their limiting values Variable Parameter Limiting value minimum Maximum x 1 Ampere conductors/m x 2 Length/pole pitch x 3 Stator slot depth/width x 4 Stator core depth in cm x 5 Average airgap flux density Wb/m x 6 Current density in the stator winding, A/mm x 7 Current density in rotor winding, A/mm A machine of power rating 3 HP with conventional design is considered for meeting with the load requirements as given in Table 3.3. The assumed loading pattern is such that the load on the motor is between 85% and 115% of the rated capacity of the motor. The design optimization is carried out for the given load curve which is the load on the machine.

13 43 Table 3.3 Assumed load cycle Duration in hours Load in kw Some parameters of the machine are taken directly from the already available design as given in Table 3.4 and fed them into the program as inputs, which modifies the rest of the parameters such that the losses are minimized and hence efficiency is maximized. Table 3.4 Design variables used as inputs Parameter Value assumed Parameter Winding factor Number of ducts provided 1 kva input 3.33 Iron loss constant for stator t teeth Stacking space factor 0.35 Number of stator slots Iron loss constant for stator core Value assumed 11W/kg 4.8W/kg 36 friction and windage loss 25W Density of iron 7600kg/m 3 Resistivity of windings Density of copper 8920kg/ m 3 Rotor slots 44 Axial slot factor 0.9 Air gap length 0.3 mm The parameters of the GA used for the present work is given in Table 3.5. The program, which is used here, is written in form of an assembly of six separate Matlab (m) files.

14 44 Table 3.5 GA parameters used in the present work Parameter Value Population size 20 Cross over fraction 0.8 Migration fraction 0.2 Cross over function Scattered Length of the string 12 bits Probability of cross over 0.8 The design parameters of the motor are optimized for optimizing the full load commercial efficiency and using the corresponding values of the constraints, new set of design parameters are obtained. The procedure is repeated for the loading pattern given in Table 3.3 such that the motor operates at its maximum energy efficiency. 3.7 RESULTS AND DISCUSSION The induction motor dimensions for both commercial efficiency optimization and energy efficiency optimization are obtained from the optimization process carried out using GA. Both sets of dimensions are compared along the initial design dimensions obtained from the conventional design. The comparison is tabulated in Table 3.6.

15 45 Table 3.6 Comparison of design parameters Design parameter Conventional design Optimized design Commercial efficiency optimization Energy efficiency optimization Diameter 0.102m m m Outer diameter m m m Length m m m Stator core depth 1.7 cm 1.0 cm cm Specific magnetic loading 0.6Wb/m Wb/ Wb/m 2 Stator slot depth/width Stator current density 4A/mm 2 4A/mm 2 4A/mm 2 Iron weight 10.5kg 6.85kg 6.73kg Copper weight 4.02kg 2.664kg 2.61kg Length/pole pitch It is very clear from the Table 3.6 that diameter, length and stator core depth are reduced in both the optimization approaches when compared the initial values from conventional design. Further, on comparing the optimized results, the dimensions obtained from energy efficiency optimization approach are lesser in comparison with those obtained from commercial efficiency approach. However, the value of flux density obtained from both the optimization approaches is higher when compared to the flux density value obtained from conventional design. This increases the specific core losses (core loss/unit volume of iron). Since, the weight of iron in optimized design is less in comparison with that from the conventional design, total iron loss is reduced. Also, since the weight of both copper and iron are reduced, the cost of the motor from both the optimization approaches will be less when compared with that of motor with conventional design

16 46 approach. Further, on comparing both the design optimization approaches, it is very clear that, energy efficiency optimization approach gives lesser dimensions and less weight. The equivalent circuit parameters corresponding to both optimization approaches are calculated and compared as shown in the Table 3.7. The values of the equivalent circuit parameters corresponding to energy efficiency optimization approach are small when compared with the corresponding values from commercial efficiency optimization Table 3.7 Comparison of equivalent circuit parameters Equivalent circuit parameter Commercial efficiency optimization Energy efficiency optimization Stator resistance 3.5 ohms 2.8 ohms Rotor resistance 3.16 ohms 2.6 ohms Mutual inductance Henry ohms Stator leakage reactance 2.17 ohms 1.98 ohms Rotor leakage reactance 2.14 ohms 2.01 ohms Further, the efficiency and slip for various loads from no load to full load for both the optimization approaches are calculated and are given in Table 3.8 along with their corresponding values from conventional design. The corresponding performance characteristics are shown in Figure 3.1. It is clear from the Figure 3.1 that the efficiency calculated from both the optimization approaches are more than the efficiency from conventional design from no load to full load. On comparing the performance of both the optimization approaches, it is clear that the efficiency of the motor designed based on energy efficiency optimization approach is more than that of the motor designed based on commercial efficiency optimization approach.

17 47 Conventional design, Commercial efficiency optimized design Energy efficiency optimized design Figure 3.1 Load Vs Efficiency characteristics Table 3.8 Comparison of performance parameters % Full load Conventional value Optimized design Commercial efficiency optimization Energy efficiency Optimization Efficiency Slip Efficiency Slip Efficiency Slip % % % % 5.35% 73.5% 2.95% 75.63% 2.85% % 5.92% 77.3% 3.00% 79.57% 2.88% % 6.23% 81.32% 3.08% 81.34% 2.95% % 6.40% 88.79% 3.15% 90.08% 2.98% % 88.33% 3.19% %

18 48 The slip of the motor for various loads is calculated as given in Table 3.8 for all the three design approaches. The machine designed based on energy efficiency optimization approach operates a lesser value of slip for all the loads. 3.8 VALIDATION OF THE RESULTS The superiority of the proposed design method is validated by comparing the results obtained from the proposed design with that available in a published work. Results obtained from Ranjith kumar. K et al(2010) was considered for the comparison. The machine under study is a 4kW motor with 4 poles. The loading pattern as given in Table 3.9 is assumed for the purpose of applying the proposed design methodology. Table 3.9 Assumed load cycle for validation of results Duration in hours Load in kw The equivalent circuit parameters from the proposed method are compared with those given in literature. The results of comparison are as given in Table Also, the efficiency of the motor designed using the proposed method is compared with those available in literature as given in Table 3.11.

19 49 Table 3.10 Comparison of Equivalent circuit parameters with those available in literature Parameter Value from literature Value from the proposed design Stator Resistance 1.15 ohms 1.16 ohms Rotor Resistance 1.44 ohms 1.2 ohms Mutual Inductance Henry Henry Stator self inductance Henry Rotot self inductance Henry Henry Henry Table 3.11 Comparison of efficiency from the proposed design with that from literature % load % efficiency from literature GA Fuzzy PSO % % % % % % efficiency obtained from the proposed method It is clear from the comparison that the efficiency at light loads calculated from the proposed design is lesser in comparison with those available in literature. However, the efficiency near rated load is more in the proposed method as compared to that available in literature. Even though the difference is marginal, the energy saving will be more over a period of time for motors designed with continuous duty cycle.

20 CONCLUSIONS Genetic algorithm is applied for finding the optimum design of the motor for tailor made applications. Machine rating is calculated for a given load cycle. For this rating, the design parameters are calculated using conventional design approach. The design of this machine is optimized for optimizing the commercial efficiency as well as for optimizing the energy efficiency using genetic algorithm. The design specifications of both conventional and optimized design are compared. The result of optimization proves that the dimensions, equivalent circuit parameters, slip and the efficiency from the optimized design are better than that of the conventionally designed machine. Also, the weight of active materials is reduced thereby reducing the cost of the machine. Further, on comparing the results of optimization from both the approaches, it is very clear that energy efficiency optimization approach gives better results. Even though the difference is marginal at full load, if the energy efficient design is adapted, it leads to reduced energy loss over a period of time. Optimization of the energy efficiency of an induction machine, using genetic algorithm is found to provide satisfactory results. Hence, for tailor made applications, the energy consumption can be optimized by adapting an exclusive GA based design algorithm for the required loading pattern. Efficient control of motor is equally important for reducing the energy loss during operation. Next section deals with a novel control scheme for robust performance of an induction motor.