Keywords

1 Introduction

Electrical motors are one of the largest electricity consumers and they are responsible for almost 45% of consumption of electrical energy. The strict efficiency regulation had come into force in EU from January 2017 that impose that all of the motors released in the EU market in power range from 0.75 to 375 kW must have efficiency class IE3. This covers efficiency levels of above 80%. On the other hand, the induction motors due to their principle of operation and construction are limited with respect to achieving high efficiency and power factor. Some of the drawbacks of the asynchronous induction motors are high magnetizing current that implies poor power factor, induction of the current in the rotor winding, usually of squirrel cage type that adds additional copper losses located in the rotor winding, lowering the motor efficiency. Usage of high quality materials such as steel with low specific losses can improve the efficiency but also contributes to the higher production costs. Power factor is another issue that is important for operation of the induction motors. Low power factor is followed by the increase of the line current and consequently with increased copper losses in the stator winding. All losses in the motor contribute to the motor heating and potentially shorten its operational life. Therefore a careful and detailed analysis regarding all design aspects of the induction motor is needed. The analysis concerning distribution of the rotor bars in squirrel cage winding and their influence on the generation of the rotor slot harmonics is described in [1]. Interesting idea regarding efficiency improvement of the induction motor with small design modification such as introduction of stator and rotor slits can be found in [2]. An important construction detail in operation of the motors is the slot fill factor and its optimization [3, 4]. The high slot fill factor of the stator slots can significantly contribute to the higher efficiency of the motor. Yet, the accurate determination of all types of losses including stray losses and friction and windage losses is very important for accurate determination of efficiency [5, 6]. Various authors propose the method of Genetic Algorithms or the improved version of it for finding the optimal values of different design parameters [7, 8]. Each computed optimized model of the motor needs a validation with experiments. The comparison of computed and measured results allows a deep insight on the capability of the mathematical model to accurately reproduce the phenomena, and consequently of predicting the device performances and in particular the power losses under different operating and supply conditions [9, 10]. Following a major constrain in optimization, output power of the motor to remain unchanged, two optimized models of the three phase induction squirrel cage motor in this paper were derived. Starting point is the old version of Končar motor 2AZ 155-4, available for testing in faculty laboratory, along with all necessary constructing details available from motor manufacturer. Based on the data from manufacturer (the motor dimensions, constructional details of steel laminations, winding type etc..), the computer model of the motor is modeled which gives as output, the motor parameters and operational characteristics (BM). Optometric analysis is run by varying the number of conductors per slot (CPS) and air gap length in order to find the best combination of CPS and air gap length that allows the best operating characteristics. The first optimized model (OM1) has improved power factor from 0.8 to 0.85 and slightly improved efficiency from 78.7% to 78.8%. The comparison is done with the starting model (BM). The real Končar motor has power factor of 0.8 and efficiency of 77.8% for 87% of the rated load, measured at the faculty’s laboratory. Second optimized model (OM2) is derived by varying the CPS, air gap length along with the modified stator slot that allows improvement of slot fill factor, increased outer diameter of the stator and the motor length. This second and final optimized model, obtained by optometric analysis as well, has achieved considerable improvement of efficiency i.e. 86.5% and power factor 0.87 while the motor output power is kept unchanged-2.2 kW. Obtained results are compared with Končar motor of IE3 class-H5AZ100LA-4. The numerical models, (FEM) models of the motors, were derived as well. The OM2 model has lower flux density in stator yoke, compared to OM1 and BM. Finally the transient characteristics of speed, torque and current are obtained for OM2 model for acceleration with the rated load, showing satisfactory dynamic behavior of the optimized model. The presented optimization methodology allows obtaining relatively simple and cost effective optimized model of the motor with increased efficiency and power factor, reduced total losses and core saturation and consequently longer service life and reliability of the motor. Moreover the proposed model has even larger efficiency at 75% load of 87.3%. At 50% load the model achieves efficiency of 86.6%.

2 Methodology and Results

2.1 Analytical Models

The available data from motor manufacturer allow exact modeling of the motor regarding its dimensions and the materials’ properties in the computer program Ansys that allows obtaining the motor parameters and operating characteristics. The obtained output results i.e. parameters and characteristics are compared with the Končar motor, type 2AZ 155-4, i.e. the old type of the motor, as the available data from the manufacturer were for this type of the motor. This comparison presented in Table 1 shows good correspondence between computer model and real motor, thus the starting model (BM) is verified as sufficiently accurate.

Table 1. Comparison between BM and motor type 2AZ 155-4.
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The equations for determining the operating characteristics are presented in (1)–(7).

The electromagnetic power Pm, or air gap power, is computed by:

$$P_{m} = 3 \cdot I_{2}^{2} \cdot R_{2} /s$$
(1)

I2 is the rotor current, R2 is the rotor resistance and s is the motor slip. Electromagnetic (air gap) torque is:

$$T_{m} = P_{m} /\omega$$
(2)

Where ω is synchronous speed in rad/s. The output mechanical torque T2 is:

$$T_{2} = T_{m} - T_{fw}$$
(3)

Tfw is the friction and windage torque. The output power is:

$$P_{2} = T_{2} \cdot \omega_{2}$$
(4)

where \(\omega_{2} = \omega \left( {1 - s} \right)\) is the rotor speed in rad/s and s is the motor slip. The input power is:

$$P_{1} = P_{2} + P_{cu2} + P_{Fe} + P_{cu1} + P_{s}$$
(5)

Pcu2, PFe, Pcu1 and Ps are rotor copper losses, iron-core losses, stator copper losses and stray loss respectively. The power factor is derived from:

$$\cos \phi = {{P_{1} } \mathord{\left/ {\vphantom {{P_{1} } {m \cdot U_{1} }}} \right. \kern-\nulldelimiterspace} {m \cdot U_{1} }} \cdot I_{1}$$
(6)

m is the number of phases. The efficiency is computed by:

$$\eta = \frac{{P_{2} }}{{P_{1} }} \cdot 100$$
(7)

Optometric analysis is set in order to find the optimal number of conductors per slot and air gap length. For that purpose variation range of CPS is defined to be from 100 to 130 and the air gap length from 0.2 to 0.4 mm. The BM model has 115 CPS and air gap length of 0.3 mm. After optometric analysis is run the optimal number of CPS is found to be 118 with air gap length of 0.2 mm, which gives the best result regarding efficiency and power factor i.e. efficiency of 78.8% and power factor of 0.85. This optimized model which is a result of first optometric analysis is called OM1. More detailed data about this model are presented in Table 2. If we compare the efficiency of BM (Table 1) and efficiency of OM1 a very slight increase can be observed. Therefore the second optometric analysis is run but in the motor model, the stator slot was modified in order to obtained bigger slot fill factor. The good slot fill factor is important for the motor efficiency. The bigger the slot fill factor is, the lower the copper losses are. The fill factor depends of the wire shape. Round shapes can only be used with limited efficiency. Other cross sectional shapes such as a rectangular one can bring improvement, but have limited applications due to its high cost and unsuitability for any but heavy gauge wires [4]. In our case the round magnetic wire is used. The usual slot fill factor is between 60–70%. The limit for the slot fill factor in the computer program is set to be 75%. In this second optometric analysis apart from the modification of the stator slot, the CPS are varied again in interval from 95 to 130, the air gap length from 0.2 mm to 0.4 mm. Additionally, two more variables in OM2 were added, motor length and outer stator diameter i.e. the motor length was varied from 100 mm to 105 mm and the outer stator diameter from 152 mm to 163 mm. The output result of this second optometric analysis is second optimized model OM2 with 92 conductors per slot, the length of air gap 0.2 mm, stator outer diameter of 163 mm and motor length of 105 mm. Data are presented in Table 2. Considerable improvement of efficiency is observed from 78.8% to 86.5% and power factor of 0.87. The slot fill factor was increased from 62.8% at OM1 to 71.3% at OM2. The data of the last optimized model were compared with the latest version of the Končar motor, type H5AZ 100LA-4 (IE3), in order to verify the second optimized model [11]. The comparisons between OM1, OM2, H5AZ 100LA-4 (IE3) as well as the newer version of Končar model 5AZ 100LA-4 (IE1 class) are presented in Table 2.

Table 2. Comparison between OM1, 2AZ 155-4 (IE1), OM2 and H2AZ 155-4 (IE3).
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Analytical calculation of the flux density in the constructing parts of the motor was done as well. Obtained results for BM, OM1 and OM2 are presented in Table 3.

Table 3. Comparison between BM, OM1 and OM2.
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From the presented results in Table 3 it is evident that the flux density in stator yoke of BM and OM1 is high which causes the core saturation and machine heating. The increase of the diameter of the stator has decreased the flux density in stator yoke and the machine heating. In terms of the flux density distribution the OM2 model is designed better than previous models of the motor. The complete distribution of the flux density in the machine cross section will be presented in the numerical models and calculated by the aid of Finite Elements Method (FEM). FEM models are created in Ansys program as well. The program allows besides analytical calculation of motor models and their optometric analysis also creation of FEM models and calculation of magnetic flux density inside the models. The cross section of BM and OM2 is presented in Fig. 1.

Fig. 1.
figure 1

Cross section of motor models

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In Fig. 2 is presented efficiency of BM, OM1 and OM2 versus output power. The key points of efficiency for 100%, 75% and 50% load are presented for OM2. The Figures should support the data in Table 2 and more clearly illustrate the operation of all three models. In Fig. 3 is presented the power factor versus output power for all three models. Finally the output torque versus speed is presented in Fig. 4. Increased efficiency in OM2 model compared to BM and OM1 is a result of the increased fill factor, due to a slot modification, the increase of power factor and consequently the decrease of the current and the copper losses. Yet, it should be noted that the air gap length in both optimized models is decreased compared to the original motor from 0.3 mm to 0.2 mm. Decreased air gap increases the power factor and efficiency but worsens the heat dissipation and motor cooling. Initially, the length of the air gap was calculated according to [12]:

$$\delta = (0.1 + 0.012 \cdot \sqrt[3]{{P_{n} }}) \cdot 10^{ - 3} {\text{m}} \approx 0.25 \cdot 10^{ - 3} {\text{m}}$$
(8)

During optometric analysis it is chosen to vary the air gap length in interval (0.2–0.3) mm in steps of 0.1 mm. As the target of optimization is efficiency the length of the air gap was reduced in the optimized model to 0.2 mm. The OM2 model was calculated also for the air gap length of 0.25 mm and satisfactory results of efficiency and power factor at rated load were obtained i.e. 86.3% for efficiency and 0.85 for the power factor. Since several variables are varied within certain limits simultaneously it is very useful to run optometric analysis in order to determine the best combination of all variables which gives the best performances of the motor. The increased efficiency of OM2 comes with the increased weight of the motor and the material consumption. Similar conclusion can be reached for Končar motors where IE3 class of the motor 2AZ 155–4 has increased weight of almost 5 kg compared to IE1 class of the same motor [11]. The OM2 model shows very good operating characteristics also at partial load (Table 2).

One of the important factors for good efficiency is good slot fill factor. In all optimized motor models, the wire diameter is automatically adjusted in order not to exceed the limited slot fill factor of 75%, set in the computer program. Yet, the operation of the motor highly depends on many design details such us good slot fill factor, air gap length, good cooling etc.… Many of these details are modified during production which affects the final operating characteristics.

The good power factor is very important for the motor operation and for the industry as electricity bills are reduced and the low power factor penalty is avoided. The system capacity is increased as additional loads can be added without overloading the system. Improved system operating characteristics are also due to the low line losses and voltage drop as a result of the lower motor current. In that respect the model OM2 shows promising results.

Fig. 2.
figure 2

Efficiency of motor models

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Fig. 3.
figure 3

Power factor of motor models

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As there is no significant difference in torque characteristics of BM and OM1 in Fig. 4 is presented torque versus speed only for BM and OM2.

Fig. 4.
figure 4

Torque of motor models

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Both optimized models OM1 and OM2 have sufficiently large starting and breaking torque. The overloading capability (break-down torque ratio) is sufficiently large and in good correspondence to IE1 and IE3 class of motors from Končar. Efficiency of the machine is highly affected by accurate determination of frictional and windage losses and stray losses. In the analyzed case of optimization, the frictional and windage losses are calculated as 1% of the motor output power while stray losses are calculated as 1.8% of the output power according to [11] and [7]. The practical measurements may differ from these assigned values.

2.2 Numerical Models

The design of electrical machines is verified usually by numerical models which determine the distribution of flux density inside the entire cross section of the machine. The Finite Elements method (FEM) is useful for detection of points of the magnetic core with high flux density which cause the core saturation and machine heating. In the standard design of the induction motor generally the flux density in the stator core may be assumed varying between 1.2 to 1.4 T. The flux density in stator and rotor teeth is limited bellow 1.8 T. According to [12] the air gap flux density for a four pole machine is recommended to be 0.65 T to 0.78 T. Yet, the final calculation of the flux density is performed by finite elements method where the motor cross section is divided into numerous elements and the magnetic vector potential is calculated in each element and consequently the flux density. In Fig. 5 is presented the flux density distribution in all three models, calculated by FEM.

Fig. 5.
figure 5

Flux density distribution

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Additional reason for the modification of stator slots was relatively large areas of stator yoke with high flux density in the BM and OM1. Taking into consideration that slot height was modified and the area of stator yoke was increased thus the flux density in stator yoke is considerably decreased from 1.98 T at OM1 to 1.26 T at OM2. Areas of high flux density are still notable at OM2 in the lower part of stator and rotor teeth. Yet, the areas of magnetic core saturation are greatly reduced at OM2 model.

2.3 Dynamic Model

Motor dynamics is an important part in analysis of motor operation. It gives an overview of motor acceleration with or without load or with a step load coupled to the motor shaft after motor has accelerated. In this paper the transient characteristics of speed, torque and current for two operating regimes: acceleration with a rated load and operation with a step load, equal to the rated load, and coupled to the motor shaft 0.5 s after the motor starting are presented, for the OM2 model. The dynamic models are derived from Simview, a software module of Ansys program. The presented transient characteristics should also verify the accuracy of the analytical model of the optimized motor-OM2. In Fig. 6 are presented transient characteristics of speed for the above mentioned operating regimes.

Fig. 6.
figure 6

Transient characteristic of speed-OM2

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From the presented characteristics of speed it can be concluded that when motor is accelerated with rated load of 14.8 Nm the acceleration time is longer, approximately 0.4 s, after which the motor reaches the rated speed of 148.8 rad/s or 1421 rpm. The obtained result for the rated speed is in good correspondence to obtained analytical value (Table 1) of 1418 rpm. When the motor accelerates at no load, the acceleration time is shorter, approximately 0.3 s, after which the motor reaches no-load speed of 156.99 rad/s or 1499 rpm. A rated load of 14.8 Nm is coupled to the motor shaft 0.5 s after motor starting. The speed decreases to the rated speed (Fig. 6b).

Fig. 7. 
figure 7

Transient characteristic of torque-OM2

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Similar conclusions can be derived for transient characteristics of torque. After motor acceleration has finished and the transients are suppressed the torque has the value of the rated torque of 14.79 Nm. For the operation with the step load the value of the torque decreases to the no-load torque after the no-load acceleration, and increases again when the step load is applied equal to the rated load (Fig. 7b).

Fig. 8.
figure 8

Transient characteristic of current-OM2

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The stator current has high starting value (50 A or rms 35.5 A) which corresponds to the rated current times eight (locked-rotor current ratio of 7.9. in Table 1). After acceleration of the motor is finished, the current decreases to the rms value of the rated current 4.4 A, or in case of the step load it decreases up to the no-load current of rms value of 2.3 A and increases again when the step load is coupled to the motor shaft, up to the rated current (Fig. 8). The comparison between transient and analytical characteristics is presented in Table 4. From the presented transient characteristics it can be concluded that motor accelerates with rated load and maintains the steady-state operation without problems. Similar conclusion can be derived also in case when the rated load is coupled to the motor shaft after the acceleration. The obtained values of torque and current are within expected limits. The similarity of the obtained values of speed, torque and current from the analytical and the dynamic model verifies the accuracy of the models and the obtained results from them.

Table 4. Comparison between analytical and dynamic model of OM2.
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3 Conclusion

The need for the more efficient electrical motors has imposed a challenging task to the motor designers. This task becomes even more complex in case of induction squirrel cage motor due to the limited possibilities for its improvement as a result of construction limitations. One of the biggest challenges for the designer is obtaining the optimal design with high efficiency, good power factor, sufficiently big overloading capability while keeping the material consumption and production costs low. Paper proposes the methodology for efficiency improvement of three phase squirrel cage motor by obtaining the best combination of outer stator diameter, motor length, stator slot design, number of conductors per slot and the air gap length in order to achieve high efficiency comparable to IE3 level, good power factor and sufficiently big overloading capability. Moreover, the same parameter of the motor has opposite impact on different operating characteristics of the motor. For example the increase of air gap length increases motor overloading capability and motor cooling but decreases the power factor. Finding the best combination of various parameters that allow obtaining the cost effective model of the motor can be done by optimization techniques i.e. in this paper is used optometric analysis of four parameters: number of conductors per slot, air gap length, outer stator diameter and the motor length, applied in the motor model with modified stator slot. All four parameters are varied in prescribed boundaries, defined on the base of the designer’s experience. From the various combinations of these four variables that give numerous motor models, the optimized model OM2 is chosen as the best solution in terms of the motor efficiency, power factor and overloading capability. The weight and the material consumption in obtained optimized model have increased compared to the starting model which certainly increases the cost of the motor. Yet, the efficiency has increased from 78.4 to 86.5% with good power factor of 0.87. Moreover, the proposed optimal model shows very good efficiency at partial load (i.e. 50% or 75% of the rated load) tending to be 86.6 and 87.3, correspondingly. The power factor of OM2 model is high, with value of 0.87 and it is considerably higher than at motor prototype from the producer. The optimized model shows good flux density distribution with very small areas of core saturation. This is mainly due to the modified stator slot and increased outer stator diameter. The drawback of this modification is the increased material consumption and cost of the motor. The optimized model OM2 has satisfactory dynamical behavior at acceleration and steady-state operation with or without load. Moreover, the obtained results of speed, current and torque from the dynamic model of OM2 show satisfactory similarity with the obtained results from analytical model of OM2 thus both models, analytical and dynamical, are verified as sufficiently accurate. From above stated, it can be concluded that motor design requires careful analysis of several major parameters that have biggest impact on motor operating characteristics. Their determination should be the results of optimization processes that are searching for the best combination of those parameters which allow obtaining the model of the motor with high performances. The optimization of the variables should be evaluated in terms of complete specter of operating characteristics, not just regarding one operating characteristic. The proposed model is theoretical, based on computer calculations and simulations. The construction of the motor prototype is affected by many factors such as influence of the air gap length on motor heating, noise and vibration, possibility to obtained high fill factor of the stator slot etc.. The motor prototype should verify the proposed model and its characteristics.