Temperature Field of Demagnetization Fault in Permanent Magnet Synchronous Generator

The temperature of the generator is mainly related to the internal losses and the thermal conductivity of the relevant materials. The PMSG has a fully enclosed surface for natural wind cooling. The heat of the generator is primarily dissipated in two ways: conveying the winding heat to the air via the stator and casing, and releasing the internal heat from the air gap to the rotor core.

2.1 Heat source distribution

The loss of the generator mainly includes the copper loss of stator windings, the stator core loss, the eddy current loss of the permanent magnets, and the mechanical loss. Among them, the mechanical loss is so small as to be negligible. By contrast, the copper loss accounts for a large portion of the total loss [19]:

${{P}_{cu}}=mI_{t}^{2}R$      (1)

where, Pcu is the copper loss of the stator windings; m is the phase number of the generator; I_tis the phase current under different degrees of demagnetization fault; R is the actual resistance of the stator windings.

Once a demagnetization fault occurs, the generator may operate asymmetrically, producing an asymmetric current. In this case, since the winding of the PMSG is made of copper, The resistivity of copper is related to the temperature of the generator and the temperature coefficient of the material itself. The temperature coefficient of copper material will also change with the temperature of the PMSG. The temperature coefficient of copper ∂ at temperature θ is [20]:

$\partial =\frac{1}{234.5+\theta }$       (2)

where, ∂ is the temperature coefficient of copper, θ is the internal temperature of the motor.

The resistance of copper is:

${{R}_{\theta }}={{R}_{20}}\left[ 1+\partial \left( \theta -20 \right) \right]$      (3)

where, R₂₀ is the resistance of copper at 20°C.

When demagnetization failure occurs, the internal temperature of the generator changes, the resistance value of the copper material also changes accordingly, which is not a constant resistance value in an ideal state. Therefore, it can be seen from formula (1) that the copper loss of winding is directly proportional to the actual resistance of stator winding, and the change of resistance value of winding resistance caused by temperature will lead to a certain error in the calculated copper loss of winding. To overcome the error, an experimental platform was built to test the input and output powers of the generators with a power analyzer, and an electromagnetic model was established to calculate the stator core loss and the eddy current loss of the permanent magnets. Then, the copper loss of the windings can be calculated by:

${{P}_{cu}}={{P}_{1}}-{{P}_{2}}-{{P}_{v}}-{{P}_{w}}$      (4)

where, P₁ and P₂ are the input power and output power of the generator respectively; P_v and P_w are the stator core loss and eddy current loss of permanent magnets respectively. Under different degrees of demagnetization fault, the P_v and P_w of permanent magnets can be solved by the electromagnetic field simulation model of the PMSG demagnetization fault. The stator core loss can be calculated by Dr. Bertotti’s iron loss separation model [21]:

$\begin{align} & {{P}_{v}}={{P}_{h}}+{{P}_{c}}+{{P}_{e}}={{K}_{h}}fB_{\max }^{2} \\ & +{{K}_{c}}fB_{\max }^{2}{{K}_{e}}fB_{\max }^{\frac{3}{2}} \\\end{align}$       (5)

where, K_h, K_c, and K_e are hysteresis, eddy current, and additional loss coefficient respectively; f is frequency; B_maxis the magnetic density amplitude. According to the hysteresis loop of the silicon steel sheet, K_h=184.23367054, K_c=0.3862605926, and K_e=0.270231418.

Table 1 lists the experimental and finite-element simulation results on the copper loss, stator core loss, and eddy current loss of permanent magnets in the PMSG under normal conditions and different kinds of demagnetization fault. Note that the demagnetization location is illustrated in Figure 4.

Table 1. Loss of the PMSG under normal condition and demagnetization fault

Table 2. Thermal conductivity of the materials (W/(m²∙K))

2.2 Thermal conductivity of materials

The generator has a complicated internal structure. The air gap between stator windings, stator, and rotor must be specialized to simplify the calculation and analysis. It is assumed that the stator slots are completely impregnated by insulating varnish, and uniformly filled with windings. Moreover, the insulation varnish of the windings is evenly distributed, and the slot insulation is closely combined with the stator slots and the copper wires, with a negligible temperature difference between the wires in the slot. On this basis, the various materials, such as the insulation varnish in the stator slots, were likened to windings with the same volume as the slot. Drawing on [8], the thermal conductivity of the windings can be calculated by:

${{\lambda }_{eq}}=\sum\nolimits_{i=1}^{n}{\frac{{{\delta }_{i}}}{(\sum\nolimits_{i=1}^{n}{\frac{{{\delta }_{i}}}{{{\lambda }_{i}}})}}}$      (6)

where, $\lambda_{e q}$ is the thermal conductivity of the windings, $\mathrm{W} /\left(\mathrm{m}^{2} \cdot \mathrm{K}\right) ; \delta_{\mathrm{i}}$ is the thickness of various equivalent materials, $\mathrm{m} ; \lambda_{i}$ is the thermal conductivity of each material, $\mathrm{W} /\left(\mathrm{m}^{2} \cdot \mathrm{K}\right)$.

The heat convection between the air gap, stator, and the rotor is realized as the air flows in the air gap under the driving effect of the rotation of the rotor. The equivalent thermal conductivity was introduced for the turbulence of the airflow in the air gap. The airflow in the air gap is comparable to a stationary fluid. Thus, the heat exchange capability of the airflow in the air gap was described with the thermal conductivity of the stationary fluid. The equivalent thermal conductivity of the air can be calculated by:

${{\lambda }_{eff}}=0.0019\cdot {{\eta }^{-2.9084}}\cdot {{\operatorname{Re}}^{0.4614\ln (3.33361\cdot \eta )}}$      (7)

where, $\eta=\frac{r_{0}}{r_{i}}, r_{0}(m)$ and $r_{0}(m)$ is the outer diameter and inner diameter of the stator, respectively; $R_{e}=\frac{n \phi_{1} \delta}{v}$ is the Reynolds number in the air gap. The value of $R_{e}$ was calculated as $25.10$.

The thermal conductivity of each part of the PMSG was derived by formulas (4) and (5). The results are recorded in Table 2.

The demagnetization fault disrupts the distribution of the magnetic field and the asymmetric operation of the PMSG, causing a change to the loss and its distribution in the generator. The generator loss directly affects the internal temperature distribution. This paper analyzes the temperature distribution and variation law of the generator under normal conditions, and three kinds of demagnetization fault: single-block 50% demagnetization, single-block complete demagnetization, and symmetric two-block 50% demagnetization.

4.1 Temperature distribution and variation law of windings and stator core

The copper loss of stator windings, accounting for the greatest part of the total loss, is the leading impactor of the temperature distribution of the generator. Figure 2 shows the temperature distribution of stator windings under normal conditions and different kinds of demagnetization fault. Under both natural conditions and demagnetization fault, the temperature peaked at the windings; the outer layer windings were slightly hotter than the inner layer windings; the lowest temperature appeared in the middle of the inner layer windings.

2a.png

(a) Normal conditions

2b.png

(b) Symmetric two-block 50% demagnetization

2c.png

(c) Single-block 50% demagnetization

2d.png

(d) Single-block complete demagnetization

Figure 2. Temperature distribution of stator windings under normal conditions and demagnetization fault

In the event of demagnetization fault, the temperature of the stator windings decreased across the board. Under single-block demagnetization, the temperature drop increased with the demagnetization degree. The temperature under symmetric two-block 50% demagnetization was 0.32% lower than that under single-block 50% demagnetization. This is because the asymmetric magnetic field distribution under single-block 50% demagnetization is more severe than that under symmetric two-block 50% demagnetization. The temperature of the windings is also affected by the stator core loss. The core loss under symmetric two-block 50% demagnetization was lower than that under single-block 50% demagnetization. That is why the winding temperature under symmetric two-block 50% demagnetization is much cooler than that under single-block 50% demagnetization.

4.2 Temperature distribution and variation law of stator core

Figure 3 shows the temperature distribution of stator core under normal conditions and different kinds of demagnetization fault. The stator core was significantly cooler than the windings. For the entire stator core, the temperature peaked on the stator teeth, and gradually fell from the teeth to the outer surface.

3a.png

(a) Normal conditions

3b.png

(b) Symmetric two-block 50% demagnetization

3c.png

(c) Single-block 50% demagnetization

3d.png

(d) Single-block complete demagnetization

Figure 3. Temperature distribution of stator core under normal conditions and demagnetization fault

As shown in Figures 3(b) and 3(c), the temperature under symmetric two-block 50% demagnetization was 0.48% lower than that under single-block 50% demagnetization, because the core loss under the former is smaller than that under the latter.

4.3 Temperature distribution and variation law of permanent magnets

High temperature is a primary cause of the demagnetization of permanent magnets. Thus, it is important to study the temperature of permanent magnets under demagnetization fault. Figure 4 shows the temperature distribution of permanent magnets under normal conditions and different kinds of demagnetization fault. The temperature of permanent magnets gradually decreases from the center to both ends, with the peak at the center surface. The occurrence of the demagnetization fault suppressed the overall temperature of permanent magnets, and the temperature drop increased with the demagnetization degree. Specifically, the temperature under symmetric two-block 50% demagnetization was 3.6% lower than that under single-block 50% demagnetization. The temperature drop of permanent magnets was deeper than that of windings and stator core undergoing the same change of demagnetization faults. This is attributable to the dominant temperature rise effect of the eddy current loss of permanent magnets. Moreover, the eddy current loss under symmetric two-block 50% demagnetization was smaller than that under single-block 50% demagnetization, and similar to that under single-block complete demagnetization. Hence, symmetric two-block 50% demagnetization and single-block complete demagnetization bore a resemblance in temperature distribution.

4a.png

(a) Normal conditions

4b.png

(b) Symmetric two-block 50% demagnetization

4c.png

(c) Single-block 50% demagnetization

4d.png

(d) Single-block complete demagnetization

Figure 4. Temperature distribution of permanent magnets under normal conditions and demagnetization fault

Figure 5 shows the peak temperature variation of windings, stator core, and permanent magnets with demagnetization degrees. The windings were always hotter than the stator core and permanent magnets, whether under normal conditions or demagnetization fault. The peak temperature of the three parts of the generator plunged with the growing demagnetization degree. The peak temperatures of windings, stator core, and permanent magnets under single-block 50% demagnetization were 0.32%, 0.48%, and 3.6% lower than those under symmetric two-block 50% demagnetization, respectively; the peak temperatures of windings, stator core, and permanent magnets under symmetric two-block 50% demagnetization were 2.97%, 2.74%, and 1.07% higher than those under single-block complete demagnetization, respectively.

5.png

Figure 5. Peak temperature variation of windings, stator core, and permanent magnets with demagnetization degrees

Targeting a 1kW PMSG, this paper carries out finite-element electromagnetic field analysis and experiment to calculate the copper loss of windings, stator core loss, and eddy current loss of permanent magnets under normal conditions and different kinds of demagnetization fault. Specifically, the thermal conductivity of materials was determined, as well as the natural heat transfer coefficient of the casing surface. Then, the authors established a 3D temperature field model for the generator under demagnetization fault, and derived the relationship between the temperatures of windings, stator core and permanent magnets, and demagnetization degree. Finally, the 3D temperature field model was verified through a temperature rise experiment. The main conclusions are as follows:

(1) The temperature rise of the generator is related to the loss. The temperature rise effect mainly depends on the copper loss of windings. In the event of the demagnetization fault, the temperatures of the windings, stator core, and permanent magnets all decrease, and the temperature drop is positively correlated with the demagnetization degree.

(2) The temperature rise effect of permanent magnets is mainly determined by eddy current loss, and partly affected by the copper loss of the windings.

(3) The growing demagnetization degree magnifies the temperature drop of windings, stator core, and permanent magnets, because the copper loss of windings, stator core loss, and eddy current loss of permanent magnets decrease with the rising demagnetization degree.

(4) Concerning the temperature variation law of the generator under demagnetization fault, the experimental result was basically consistent with the simulated result, with an error within -2.4%~3.2%. Hence, the observed temperature variation law provides a theoretical basis for determining demagnetization fault.