Abstract:

Parameter estimation of an induction motor was carried out in conventional methods in order to determine the steady state equivalent circuit parameters. In conventional method, we obtained the parameters of an induction motor by no-load and blocked rotor test. The results obtained from the tests may not give accurate values of the parameter and it have a wide variation in the operating condition. Though the obtained parameters using conventional methods was not precise and effective when analyzing the machine for dynamic conditions so we are in the urge to adopt any other methodologies which make the estimation of parameters precise. Parameter estimation of an induction motor is carried out using soft computing methodologies is one of the way to implement for better efficiency. In the proposed scheme we presents a new algorithm based on the Artificial Bee Colony (ABC) to optimize the parameters of an Induction Motor. The proposed approach will be compared with the conventional method in order to interpret the efficiency.

1. Introduction

Induction machines are the mostly used motors in industry due to their low price and ruggedness. Induction motors(IM) have important problems, such as transient and quasi-steady state stability. To solve steady-state stability problems of induction motor, equivalent circuit parameters are required. These parameters are resistances and reactances of stator and rotor, including magnetizing branches. Estimation of these parameters is particularly essential in determining their effects on motor performance. About 60% of the industrial electric energy is converted into mechanical energy by means of pumps, fans, adjustable speed drives and the machine tools equipped with induction motors. Thus many researchers have focused on topics like modeling and parameter estimation of induction motors. The main problem of induction motor parameter estimation is the unavailability of manufacturer data to construct accurate models. Due to this reason, the induction motor models are not explicitly represented in various applications. The parameters of induction motors can be determined by common no-load and locked rotor tests. The main disadvantage of this method is that the motor has to be locked mechanically and tests have to be carried out by skilled operators. The parameter values obtained by the classical approaches can reveal signi’cant differences in the entire range of slip .This leads to the conclusion that to describe the performance of the induction machine more precisely and to reduce the differences between the estimated and real performances, one must modify the parameters obtained from the classical method. To achieve this goal, the use of optimization techniques seems to be a promising alternative to the classical approaches. Recently, in solving induction motor parameter estimation problems, some new global optimization techniques such as Evolutionary Algorithm(EA), Genetic Algorithm(GA), Differential Evolution(DE) ,Particle Swarm Optimization(PSO), Immune Algorithm(IA) have been proposed. In this research, the optimal parameter of the equivalent circuit of three-phase induction machine is suggested by Artificial Bee Colony (ABC) algorithm.

2.Problem Formulation

An Induction motor can be modeled by using an approximate circuit model,an exact circuit model. The parameter estimation problem is formulated as a least squares optimization problem, the objective being the minimization of deviation between the estimated and the manufacturer data. To achieve this utilizing the torque equation of the induction motor and the problem formulation is discussed for the two model.

2.1 Approximate Circuit Model:

Approximate circuit model of an induction motor is shown in Figure 1. In this model, R1 is the stator winding resistance,R2 is the rotor resistance referred to the stator side,X1 is the combined stator and rotor leakage reactance,Xm is the magnetizing reactance referred to the stator side,I1 is stator current,I2 is rotor current referred to the stator side,Vph is terminal voltage and s is the motor slip. The magnetizing reactance (Xm) can be eliminated from this model, because it has no effect on the rotor current and motor torque and power. Thus, the aim is to estimate R1, R2 and X1 by using the starting torque, the maximum torque and the full load torque of the motor given by the manufacturer along with the motor slip and terminal voltage.

2.1.1 Objective function:

Using the approximate circuit model of an induction motor:

Fig-1.Approximate Circuit Model

Where s, ??s,Vph are known (??s is the synchronous speed). Tf1(cal), Tlr(cal), Tmax(cal) are full load torque, locked rotor torque and maximum torque respectively that are calculated by estimating R1,R2′,X1. For this,the objective function is as follows:

where are Tf1(mf), Tlr(mf), Tmax(mf) full load torque, locked rotor torque and maximum torque given by the manufacturer respectively. For the optimum estimation of unknown parameters, we should minimize the objective function ‘F’.

2.2 Exact Circuit Model:

Exact circuit model representing the steady state operation of an induction motor is shown in Figure 2. At this model X1 is stator leakage reactance and X2′ is rotor leakage reactance referred to the stator side. Other parameters of this model are the same as approximate circuit model.

In the conventional technique, by performing the direct current test, we can find each phase resistance of the stator winding (R1). This test should be performed by the dc voltage supply because of preventing of the inductive effect in the stator winding. By performing the no load test,(X1+Xm) is found. This test performs under rated voltage and frequency.

By the locked rotor test (X1+X2′) and locked rotor resistance (RLR) are found. This test performs by locking the rotor and under a voltage that is much less than rated value. By knowing X1=X2’and RLR=R1+R2′ , the unknown parameters X1,X2′,Xm,R2′ are obtained individually. These tests can not implement easily and they need dc voltage supply, the voltage supply with tunable voltage and frequency, voltmeters, ammeters, watt meters and external element for locking the rotor. Beside it takes much time. By formulation of the parameter estimation of induction motor, these parameters can be found easily with high accuracy. The problem formulation uses the starting torque, the maximum torque, the full load torque and the full load power factor given by the manufacturer along with motor slip and terminal voltage to estimate the stator resistance, the rotor resistance, the stator leakage reactance, the rotor leakage reactance and the magnetizing reactance by proposed methods.

Fig-2 Exact Circuit Model

The objective function is as follows:

2.2.1 Objective function

At the exact circuit model of an induction motor:

Where s, ??s,Vph are known. Tf1(cal), Tlr(cal), Tmax(cal),pf(cal) are full load torque, locked rotor torque and maximum torque and power factor respectively that are calculated by estimating R1,R2′,X1,X2′ and Xm. Objective function is as follows:.

For optimum estimation of unknown parameters, we should minimize the objective function ‘F’.

2.3 Deep bar circuit model formulation:

The problem formulation uses the starting torque, maximum torque, full load torque, full load current and full load power factor manufacturer data to estimate the parameters of beep bar circuit model. The equivalent circuit for a deep bar or double cage induction motor model is shown in Fig. 3.

3.Artificial Bee Colony Algorithm

3.1 Fundamental of Artificial Bee Colony Algorithm:

Swam Intelligence (SI) is an emerging field in Artificial Intelligence (AI). The living nature and life style of animals, birds and other living organisms can be inherited and applied to solve many real world problems. ABC is a recently developed swam intelligence algorithm developed by Dervis Karaboga in the year 2005.In ABC, foraging is one of the behavior of honey bees to search, collect food from its food resources. Many research works has undergone about foraging behavior and it is applied to solve variety of optimization problems.

The minimal model of swarm-intelligent forage selection in a honey bee colony which the ABC algorithm simulates consists of three kinds of bees: employed bees, onlooker bees and scout bees. Half of the colony consists of employed bees, and the other half includes onlooker bees. Employed bees are responsible for exploiting the nectar sources explored before and giving information to the waiting bees (onlooker bees) in the hive about the quality of the food source sites which they are exploiting. Onlooker bees wait in the hive and decide on a food source to exploit based on the information shared by the employed bees. Scouts either randomly search the environment in order to find a new food source depending on an internal motivation or based on possible external clues.

3.2 Description Of ABC Algorithm:

Using the analogy between emergent intelligence in foraging of bees and the ABC

algorithm, the units of the basic ABC algorithm can be explained as follows:

3.2.1. Producing Initial Food Source Sites:

If the search space is considered to be the environment of the hive that contains the food source sites, the algorithm starts with randomly producing food source sites that correspond to the solutions in the search space. Initial food sources are produced randomly within the range of the boundaries of the parameters.

where i = 1. . .SN, j = 1. . .D..SN is the number of food sources and D is the number of optimization parameters. In addition, counters which store the numbers of trials of solutions are reset to 0 in this phase.

After initialization, the population of the food sources (solutions) is subjected to repeat cycles of the search processes of the employed bees, the onlooker bees and the scout bees. Termination criteria for the ABC algorithm might be reaching a maximum cycle number (MCN) or meeting an error tolerance.

3.2.2 Sending Employed Bees To The Food Source Sites:

As mentioned earlier, each employed bee is associated with only one food source site. Hence, the number of food source sites is equal to the number of employed bees. An employed bee produces a modification on the position of the food source (solution) in her memory depending on local information (visual information) and finds a neighboring food source, and then evaluates its quality. In ABC, finding a neighboring food source is defined by

Within the neigbourhood of every food source site represented by xi, a food source vi is determined by changing one parameter of xi. In Eq. (2), j is a random integer in the range [1,D] and k ?? {1, 2, . . .SN} is a randomly chosen index that has to be different from i.??ij is a uniformly distributed real random number in the range [-1, 1].

As can be seen from Eq., as the difference between the parameters of the xi,j and xk,j decreases, the perturbation on the position xi,j decreases. Thus, as the search approaches to the optimal solution in the search space, the step length is adaptively reduced. If a parameter value produced by this operation exceeds its predetermined boundaries, the parameter can be set to an acceptable value. In this work, the value of the parameter exceeding its boundary is set to its boundaries. If xi > xi max then xi = xi

max .If xi < xi min then xi = ximin.

After producing vi within the boundaries, a fitness value for a minimization problem can be assigned to the solution vi by

where fi is the cost value of the solution vi. For maximization problems, the cost function can be directly used as a fitness function. A greedy selection is applied between xi and vi , then the better one is selected depending on fitness values representing the nectar amount of the food sources at xi and

vi. If the source at vi is superior to that of xi in terms of profitability, the employed bee memorizes the new position and forgets the old one. Otherwise the previous position is kept in memory. If xi cannot be improved, its counter holding the number of trials is incremented by 1, otherwise, the counter is reset to 0.

3.2.3 Calculating Probability Values Involved In Probabilistic Selection:

After all employed bees complete their searches, they share their information related to the nectar amounts and the positions of their sources with the onlooker bees on the dance area. This is the multiple interaction feature of the artificial bees of ABC. An onlooker bee evaluates the nectar information taken from all employed bees and chooses a food source site with a probability related to its nectar amount. This probabilistic selection depends on the fitness values of the solutions in the population. A fitness-based selection scheme might be a roulette wheel, ranking based, stochastic universal sampling, tournament selection or another selection scheme. In basic ABC, roulette wheel selection scheme in which each slice is proportional in size to the fitness value is employed.

In this probabilistic selection scheme, as the nectar amount of food sources (the fitness of solutions) increases, the number of onlookers visiting them increases, too. This is the positive feedback feature of ABC.

3.2.4 Food Source Site Selection By Onlookers Based On The Information Provided By Employed Bees:

In the ABC algorithm, a random real number within the range [0,1] is generated for each source. If the probability value (pi in Eq. (4)) associated with that source is greater than this random number then the onlooker bee produces a modification on the position of this food source site by using Eq. (2) as in the case of the employed bee. After the source is evaluated, greedy selection is applied and the onlooker bee either memorizes the new position by forgetting the old one or keeps the old one. If solution xi cannot be improved, its counter holding trials is incremented by 1, otherwise, the counter is reset to 0. This process is repeated until all onlookers are distributed onto food source sites.

3.2.5 Abandonment Criteria: Limit And Scout Production

In a cycle, after all employed bees and onlooker bees complete their searches, the algorithm checks to see if there is any exhausted source to be abandoned. In order to decide if a source is to be abandoned, the counters which have been updated during search are used. If the value of the counter is greater than the control parameter of the ABC algorithm, known as the ”limit’, then the source associated with this counter is assumed to be exhausted and is abandoned. The food source abandoned by its bee is replaced with a new food source discovered by the scout, which represents the negative feedback mechanism and fluctuation property in the self-organization of ABC. This is simulated by producing a site position randomly and replacing it with the abandoned one. Assume that the abandoned source is xi, then the scout randomly discovers a new food source to be replaced with xi. This operation can be defined as in (1). In basic ABC, it is assumed that only one source can be exhausted in each cycle, and only oneemployed bee can be a scout. If more than one counter exceeds the ”limit’ value, one of the maximum ones might be chosen programmatically.

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