Asynchronous machines are predominantly preferred in industrial sectors for its reliability. Power quality perturbations have a greater impact on industries; among the different power quality events, voltage fluctuations are the most common and that may cause adverse effect on machine's operation since they are longer enduring. The article discusses a numerical technique for evaluating asynchronous motors while taking into account magnetic saturation, losses, leakage flux, and voltage drop. A 2D linear analysis involving a multi-slice time stepping finite element model is used to predict the end effects. As an outcome, the magnetic saturation and losses are estimated using a modified 2D nonlinear time-stepping finite element formulation. The method takes the electromagnetic fields at the ends of the motor into account using limited computer resources. The proposed method will greatly reduce computation time with limited computer resources for analyzing the machine's performance with high precision. The analyzed findings assist in preventing voltage variance issues in the power network system and provide suggestions for developing a robust system.

It is well-known fact that more than 50 percent of global electrical energy is utilized by electrical machines, especially by asynchronous machines. The induction machine is known as asynchronous machine, actually it is a more precise designation. Asynchronous machines are engaged with various industrial applications including, blowers, air conditioning systems, pumps, refrigeration, materials processing and manufacturing sectors. Three-phase asynchronous machines (AM) are widely preferred as they are reliable, robust, self-starting, and require less maintenance. Nevertheless, the power quality problems in grid are inevitable, even in advanced power networks. Hence, most of the industries are influenced by power quality perturbations. IEEE 1159–2019 defined the power quality problems as transients, sag, swell, interruptions, voltage fluctuations, waveform distortion, voltage variations, voltage imbalance and power frequency variations [

Thus, the performance study of AM under power perturbations becomes more vital. Various types of analysis including magneto-static analysis, time-harmonic analysis, electrostatic analysis, current flow analysis, and thermal stress analysis are performed on AM [

The machine's performance is degraded by voltage variations in the electrical grid, and it could trip the system, causing economic loss to industries due to outages. The voltage fluctuation has the potential to affect machine characteristics such as overheating, noise, torque oscillation, vibrations, excessive slip losses, and machine efficiency [

Performance of asynchronous machines under voltage fluctuation using FEM analysis.

Two-dimensional FEM analysis of magnetic flux density, iron loss density, joule loss density, and relative permeability as a function of voltage.

Sensitivity study on asynchronous machines under various voltage circumstances.

The losses of a textile spinning mill motor subjected to a 10% voltage variation were assessed in a case study.

The article is constructed as; Section 2 deals about generalized magnetic circuit modelling of three phase asynchronous machine with the design parameters. Section 3 describes about the finite element model analysis of 9.2 kW asynchronous machine to explore the magnetic saturation. This section explains how the FEM algorithm works in detail. Section 4 interprets the finite element analysis for a 9.2 kW asynchronous machine and determines its performance under voltage fluctuation. This section also includes a two-dimensional FEM study of magnetic flux density, iron loss density, joule loss density, and relative permeability as a function of voltage. The sensitivity study of asynchronous machines under various voltage circumstances is presented in Section 5. A case study for a textile spinning mill with a 10% voltage fluctuation was developed in Section 6, and their losses were evaluated. Finally, the paper is concluded in Section 7.

For the design of asynchronous devices, this session presents a simplified magnetic circuit model. Traditional methods to asynchronous machine design have been used, but they may be inadequately accurate or simplified while taking pole–slot counts into account. As a consequence, the early design stage's layout precision will suffer. Furthermore, since it is hard to ascertain the flux in individual stator teeth, magnetic saturation is often skipped or balanced by correction factors in generalized models. Using the established FEM model, the flux provided by stator winding currents can be measured efficiently and consistently while taking saturation into consideration. The stator side windings are similar with sinusoidally distributed type windings, placed 120° apart, where N_{s} and R_{s} are the equivalent turns and resistance of the stator, respectively [_{sr} is the magnitude of the mutual inductances between the windings.

The flux linkages can now be stated as

The voltage equations in terms of machine variables referred to the stator winding is given by,

The quantitative accuracy of the air-gap magnetic flux density distribution, however, becomes inadequate when the degree of magnetic saturation by the leakage flux is high [

The flux density (B) in air gap is given as

Here, F-MMF and P-Permeance-. The total F is expressed as

Here,

_{1}-stator turns per phase, f_{w1}-stator fundamental winding factor, g-air-gap length, and kc-carter's coefficient. P-Number of poles, and m-number of phases. D_{sc} is the inside diameter of stator core, c is the axial length of rotor core and

An electric motor consists of the electrical and mechanical system and requires an equation that couples both.

_{L,} and the angular velocity of the rotor is denoted by

Recently, Finite Element Analysis (FEA) has been mostly used in the machine's analysis and design. To explore the magnetic saturation of 3-phase AM through analyzing the air gap flux component with respect to voltage variation, the finite element model is generated. The voltage variations hardly cause saturation of the entire magnetic circuit; besides, it could produce local saturation in the stator tooth of the motor [

Description | Value | Description | Value |
---|---|---|---|

Rated power | 9.2 kW | Rated speed | 1460 rpm |

Frequency | 50 Hz | Rated voltage | 230 V |

Number of stator Slot | 36 | Slot type | Parallel |

Inner diameter | 83.5 mm | Stacking factor | 0.97 |

Outer diameter | 131 mm | Winding arrangement | Star |

Number of phases | 3 | Number of poles | 4 |

Conductors per slot | 135 | Number of winding layers | Single |

Rotor slot/bar | 28 | Air gap length | 0.25 mm |

Inner diameter | 100 mm | Stacking factor | 0.97 |

Outer diameter | 130 mm | Rotor bar skew | 12.86 grad |

Shaft diameter | 27 mm | End ring thickness | 20 mm |

Iron core | NO20 Suracognent silicon steel |

This analysis consists of a no-load test and load test is based on the calculation of equivalent circuit parameters of the AM. The equivalent circuit is shown in _{2} = 0), the stator current is basically equal to the magnetizing current. The load test is based on the nonlinear time-harmonic FEA. The accuracy of the FEA solution is defined by convergence tolerance of the FEA solution field; the default value is 1e-005. The RMS phase current, supply frequency, and rotor speed (or slip) is defined. By default, the speed is set to zero, so the standard locked rotor test can be performed. During the load test, the parameters of the equivalent circuit is computed. The motor parameters are computed assuming that L_{1}, L_{2}, R_{1}, R_{2}, and R_{m} do not change while L_{m} changes depending on the magnetizing current according to no-load test data. In reality, L_{1}, L_{2}, R_{2}, and R_{m} values more or less depending on rotor speed and saturation. AC Analysis is based on the time-harmonic FEA and the equivalent circuit but provides more accurate results comparing with equivalent circuit analysis since it can take into account variation of equivalent circuit parameters at different operating conditions. AC Analysis is performed for the specified operating points defined by the power supply (3-phase voltage source or 3-phase current source), RMS phase voltage (RMS phase current), and supply frequency fields. The speed can be defined whether by the number of rotations per minute or by slip.

Time harmonic finite element method is centered on the assumption of the sinusoidal time-dependence of the field, which allows the computation time to be reduced radically comparing with the stepping FEM [

Here, tol-convergence is the tolerance setting the desired accuracy of the solution, the generalized algorithm used in motor analysis for a nonlinear instance of the time-stepping process is shown in

Gauss-newton iteration continues until the inequality is satisfied [

The paper analysis the three-phase asynchronous motor, fed by a symmetrical three phase voltage sources with 10 percent variation. The two different FEA approaches, showing their main characteristics; 1. FEA method for the indirect test simulation2. FEA method for the load tests simulation. Both methods use fixed mesh and eddy current models, they do not consider the field harmonics and they are applied to the same two-dimensional (2D), domain ‘D’.

The field components are supposed varying sinusoidally in time. Thus in a Cartesian coordinate system (x, y, z) the values of the generic quantity G(P, t), in the point P = (x, y, z) and at the instant t, can be written as;

It is supposed that the current density vector J and the magnetic potential vector A have only the z-axis components, i.e., J = (0, 0, J_{z}) and A = (0, 0, A_{z}). Thus, magnetic field strength H and flux density B have only components, on the (x, y) plane perpendicular to the z-axis, i.e., H = (H_{x}, H_{y}, 0) and B = (B_{x}, B_{y}, 0). In this way the induction motor analysis may be realised by a 2D finite element analysis, simpler than a three-dimensional (3D) one, without a significant loss of accuracy. The 3D effects have been by suitable circuit elements outside the field solution. The sensitivity of the variables to change in voltage is studied in the sensitivity analysis part of the paper.

In this first case, the induction motor is modelized by a simplified equivalent circuit

Parameters | 0% VV | 10% UV | 10% OV |
---|---|---|---|

Rotor speed (rpm) | 1410 | 1410 | 1410 |

Rotor slip (%) | 6% | 6% | 6% |

Supply frequency (Hz) | 50 | 50 | 50 |

Torque (N-m) | 15.79 | 13.70 | 17.68 |

RMS phase current (A) | 7.86 | 5.68 | 10.84 |

PMS phase voltage (V) | 230.00 | 207.00 | 253.00 |

Input electrical power (W) | 3109.80 | 2474.93 | 3983.02 |

Output mechanical power (W) | 2331.62 | 2024.18 | 2610.66 |

Efficiency (%) | 74.97 | 81.78 | 65.54 |

Power factor | 0.57 | 0.69 | 0.48 |

Total loss (W) | 792.33 | 467.9 | 1386.53 |

Rotor cage loss (W) | 147.92 | 128.108 | 165.73 |

Stator winding loss (W) | 635.51 | 332.09 | 1210.77 |

Iron core loss (W) | 8.89 | 7.70 | 10.02 |

The objective of the analysis is to determine the extent to which flux can be routed in the asynchronous machine to achieve an electronically adjustable output voltage. The flux distribution will be observed around the windings and in each slot. The method chosen for analysis will be simulation using the Finite Element Method. The FEM software package Motor Analysis-IM is used. Ideally a method is required that allows analysis of nonlinear magnetic circuits with three voltage level. Airgap distribution plot allows the view of the distribution of the different parameters such as flux and MMF over the machine air gap beside the air gap harmonic components. The results are obtained for a selected power supply, supply frequency, and slip/speed.

The full cross-section view has been zoomed to show the pattern of distribution of flux lines in the machine. Flux lines are plotted so that the closeness of the flux lines indicates the magnitude of the flux density x-axis and y-axis limits will be determined by the size of the machine's cross-section. Z-axis limits field sets the color scale limits to a specified minimum and maximum values. Values between z-axis limits are linearly mapped to the used color scale (color map). Data values less or greater than specified z-axis limits are mapped to the minimum limit or to the maximum limit, respectively. It is clearly visible from the cross-section plot of magnetic flux density that the magnetic flux density increases with an increase in voltage and decreases under voltage. This is evident from the color scaling. During 10 percent under voltage, the flux density is less in the stator and rotor when compared to the 10 percent over voltage, where the flux density value is higher viewable from the color change of area with pale green to bright yellow under 10 percent over voltage. The increase in flux density also results in an increase in iron losses. The iron losses increase and decrease with overvoltage and under-voltage, respectively, as evident from the color change of the iron loss plot from light blue to greenish-blue in

The joule loss density is the copper losses that occur in the windings of the IM. It is also called the I^{2}R loss and is the main source of heat generation in the AM. The joule loss is very sensitive to variation in supply voltage. There is a sharp rise in copper losses under overvoltage and a reduction in losses under 10 percent UV. This can be clearly observed from

A sensitivity analysis is performed in this paper under various voltage conditions. This research is carried out to see how design variables (such as the air gap) affect the electrical parameters [

The supply voltage variation has a considerable effect on almost all performance variables. The performance variables like stator winding loss and total loss are highly sensitive with respect to 10% OV and moderately sensitive to 10% UV. Furthermore, the sensitivity of phase current, power factor, and input power are moderately sensitive with respect to 10% UV and 10% OV. Torque, output power, efficiency, rotor cage loss, and iron loss are less sensitive with respect to 10% UV and 10% OV. From the above observation, it is clear that 10% OV has a maximum effect on the performance variables. Hence, we can conclude that the AM is prominently affected more by overvoltage than under voltage. Transient Analysis is based on the time-stepping FEA and has the highest accuracy among other analysis methods allowing to take into account rotation of the rotor, cogging torque, higher harmonics, PWM switching and etc. However, this type of analysis takes considerably more time comparing with previous two analysis types (equivalent circuit and AC analysis). Transient Analysis uses Simulation script file---MATLAB-function which is called on each simulation time step and allows the user to change all simulation settings. The magnetic flux density and energy density distribution plots are shown in

Performance Variables | 10% UV | 10% OV |
---|---|---|

Torque (N-m) | 13.18% (↓) | 11.96% (↑) |

RMS phase current (A) | 27.71% (↓) | 38.03% (↑) |

Input electrical power (W) | 20.41% (↓) | 28.07% (↑) |

Output mechanical power (W) | 13.18% (↓) | 11.96% (↑) |

Efficiency (%) | 9.080% (↑) | 12.57% (↓) |

Power lactor | 22.29% (↑) | 15.62% (↓) |

Total loss (W) | 40.94% (↓) | 74.99% (↑) |

Rotor cage loss (W) | 13.39% (↓) | 12.04% (↑) |

Stator winding loss (W) | 47.74% (↓) | 90.52% (↑) |

Iron core loss (W) | 13.41% (↓) | 12.76% (↑) |

(↑) |

Here, E_{Nom} is total energy losses under nominal condition (0% VV) in kWh, E_{UV} is total energy losses in under voltage condition (10% UV) in kWh, E_{OV} is total energy losses in under voltage condition (10% OV) in kWh, n-number of samples, _{Nom}_{UV}_{OV}

In this part, a spinning machine in the textile industry is considered and studied in terms of energy conservation analysis. The textile mill uses a variety of processes such as combing, carding, spinning, and so on, with the spinning process accounting for 50% of overall energy consumption [

Taking the process cycle of the spinning frame in a textile manufacturing driven with 9.2 kW. From the results, noted that the machine with 10 percent over voltage creates 18,93,672 kW losses per year, which is almost 101.4 percent losses increased from the nominal value. Whereas, the AM with 10 percent under voltage creates 4,80,217 kW losses per year, which is almost 48.9 percent losses decreased from the nominal value.

A detailed analysis of the AM under the effect of power quality perturbations of 10% overvoltage and 10% under voltage was done. The effect of variation in voltage on the various performance variables and the distribution of magneto-static quantities in the airgap and cross-section have been studied in detail. Further, sensitivity function was used to determine the sensitivity analysis of the performance parameters like input power, efficiency, current, power factor, torque, power factor, output power, cage, iron, stator winding, and total loss of AM corresponding to voltage variations by using FEA simulations with the help of motor analysis tool in MATLAB. By sensitivity analysis, the impact of parameter variations in IM is analyzed. The 10% UV and 10% OV have a considerable effect on almost all performance variables. The AM is worst affected by 10% OV than 10% UV. An overall view of the AM behavior was acquired, and the results of the analysis are very useful in the design of an AM that can withstand the expected variation of the parameter, which in turn can lead to giving the best performance, long machine life, less machine damage to AM and satisfy the load for various application.

This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program.