Electromagnetic and Mechanical Stress Analysis of a 5 MW High-Pole Non-Overlap Winding Wound-Rotor Synchronous Wind Generator

Abstract

Utilizing non-overlap windings has emerged as a favourable choice for minimizing electrical machine manufacturing costs, among other benefits. Nevertheless, it is widely acknowledged that these windings exhibit a notable level of harmonic contents in the resultant magnetomotive force, which can detrimentally impact machine performance, particularly in terms of torque ripple. In the context of wind energy conversion, maintaining low torque ripple is an essential and demanding prerequisite. Medium-speed wind generators present a good trade-off between high energy yield and low gearbox ratios. So far, medium-speed non-overlap winding wound-rotor synchronous generator (WRSG) technologies have been limited to 10/12 and the less common 16/18 pole/slot combinations. In this study, the analysis of a high-pole number combination (24/27 pole/slots) non-overlap WRSG is carried out to theoretically and comparatively predict the electromagnetic and radial force mechanical stress performance analysis with the 16/18 machine with a phase-shifted non-overlap winding (PSW), at 5 MW power level. The study, which is founded on the finite element analysis (FEA) technique, shows that the 24/27 machine exhibits comparable average torque and torque ripple, lower core losses and significantly reduced radial forces compared to the 16/18 PSW-WRSG. However, the 16/18 PSW-WRSG has a 50% reduction in the radial forces compared to the conventional 16/18 non-overlap winding. Experimental vibration analysis of a 3 kW 16/18 WRSG test machine confirms the radial force and vibration reduction in the phase-shifted winding.

1. Introduction

As the world lessens its reliance on fossil fuels and drives the development of various renewable energy systems, wind energy systems exist as the fastest-growing and dominant renewable energy technology [1]. Geared wind generators operating at high speeds (exceeding 500 r/min) have been prevalent in the wind industry due to their compact size and reduced weight. However, a notable drawback of these generators lies in their intricate gearbox design requiring at least three stages. On the other hand, low-speed wind generators require no gearbox, but lower speeds mean that the wind generators are extremely large and therefore costly [2]. Medium-speed systems provide a suitable trade-off between high- and low-speed systems. These wind generators only need gearboxes with low gear ratios and still provide high energy yield [3].

As the world moves towards more sustainable solutions across all industries, wind energy systems are not exempted. Permanent magnet synchronous generators (PMSGs) have continued as a favoured choice for wind energy systems, but these machines require rare-earth materials, making them a less sustainable option for the future [2,4]. As such, wound-rotor synchronous generators (WRSGs) have received some renewed attention as a feasible environmentally friendly option without the use of rare-earth materials. WRSGs feature low-cost designs and possess a capability to vary flux that enables control of reactive power without the addition of extra components, crucial for seamless integration with the electrical grid [5].

The adoption of non-overlap winding (NOW) presents an opportunity to minimize material costs and the accompanying labour costs, particularly in the case of large electrical machines operating in the MW range. NOW machines, characterized by low slot numbers and low coil numbers, offer a means to further reduce manufacturing expenses compared to overlap winding (OW) machines. It is worth noting that NOW machines result in a magnetomotive force (MMF) spectrum with higher harmonic content when compared with OW machines, owing to the lower values of slots per pole per phase [6,7,8,9]. The abundance of MMF harmonics leads to increased core losses, particularly significant in large-scale machines and resulting in elevated torque ripple. Maintaining minimal torque ripple, typically below 5%, is essential to mitigate vibrations in the drive train of wind energy conversion systems.

Previous research has been carried out to develop a 3 MW 16/18 pole/slot WRSG for wind energy conversion systems connected directly to the grid [10,11]. Several methods exist to reduce MMF harmonics in NOW machines. Reference [12] proposes that the disparity in harmonic content of the MMF spectrum between single-layer and double-layer windings indicates that multi-layer windings might further reduce sub-harmonics. To test the theory, a four-layer winding configuration was designed for the stator of a 10/12 pole/slot machine and an 8/9 pole/slot machine in [12], with the latter corresponding to the 16/18 pole/slot structure. Regardless of the additional cost and complexity, the four-layer winding was found to reduce all MMF harmonics, including the main harmonic. For context, the winding factor of the fourth working harmonic in the 8/9 pole/slot machine lowered from 0.945 pu to 0.888 pu with the first iteration, while it resulted in a working harmonic of 0.931 pu with the second version.

The idea of using coils with varying numbers of turns in non-overlap windings to enhance the MMF waveform was initially explored in overlap windings. Heller et al. in [13] designed an overlap winding using a combination of two turn numbers so that all slots contained two coil sides with an N1/N2 turns ratio. However, the MMF waveform enhancement was not substantial compared to the higher winding complexity and manufacturing costs.

As non-overlap fractional slot concentrated windings have gained popularity, this strategy has seen renewed interest. In NOW technologies, each tooth is wound separately, making the use of different turn numbers per coil practically feasible. Studies in [14,15,16,17] have shown improvements in the working harmonic of their prototypes. However, this method does not reduce harmonics of higher orders and is restricted to certain pole/slot combinations.

Stator shifting has also been explored as a technique to reduce MMF harmonics of the sub- and higher orders. Dajaku and Gerling in [18] introduced a form of stator shifting for a 14/12 pole/slots machine, where the stator slots are doubled, resulting in two separate windings from the original winding. The harmonic reduction technique in [10,11] was developed to reduce the MMF sub- and higher-order harmonics without reducing the main harmonic of the machines, leading to improved machine performance, lower losses and torque ripple.

Although the machines in [10,11] show a significant improvement in performance, a major concern was raised over the balancing of radial forces of the 16/18 pole/slot combination. This pole/slot combination results in two machine sections in the model. Large machines are susceptible to large radial attraction forces between the stator and rotor [19,20,21]. The low number of machine sections translates to more imbalance in the machine’s higher radial forces. These radial forces then worsen noise and vibration in the machine, which is not desirable for wind energy conversion systems [20]. Increasing the number of machine sections provides better balancing in the machine and the ensuing radial forces. To this end, maintaining the same poles per slot per phase, which is 0.375 for the 16/18 machine, the 24/27 pole/slot combination is considered in this study. This combination then results in three machine sections but still maintains a NOW structure. WRSGs are typically preferred by industry for high power, 10 MW and larger, wind energy conversion applications where reactive power control is crucial [2,18]. Increasing the competitiveness of WRSGs at lower power levels to extend their suitability is an ongoing task.

Consequently, the theoretic and comparative prediction of the electromagnetic and radial force mechanical stress performance analysis is applied to a 5 MW NOW-WRSG with a high-pole number. No such study currently exists in available literature for the 16/18 or 24/27 NOW-WRSGs. The effect of the phase-shifting technique on the radial forces has also not been analyzed previously in the literature and is therefore unique and novel to this study. The proposed NOW-WRSG is designed for a medium-speed wind generator system and provides a means to establish the effect of balancing of radial forces and applying the finite element analysis (FEA) technique to predict the stability of the machine. To this end, the current study presents the novel 24/27 pole/slot NOW-WRSG configuration and also provides electromagnetic analysis and comparison of the radial forces with a 16/18 pole/slot machine, both with and without phase-shifting winding techniques.

The rest of the paper is organized as follows: Section 2 is used to present, analytically model and characterize the basic electromagnetic performance of the proposed NOW-WRSG. Section 3 is then used to perform and compare the mechanical stress analysis between the proposed machine and existing structures. Section 4 presents some experimental analysis and discussion. Lastly, some concluding remarks are given in Section 5 based on the key findings.

2. Initial Model Characterisation and Modelling

The 16/18 pole/slot WRSG from [10] is used as the basis for the comparison. The 24/27 pole/slots NOW-WRSG is designed using classical machine design equations and assumptions. FEA is conducted with in-house software called SEMFEM 3.8.1 and supported by a commercial package, ANSYS Maxwell 2020 R2. Both models have been optimized using NSGA-II. The 2D FEA depictions of the two 5 MW WRSG three-phase machines are displayed in Figure 1.

Table 1. Technical and dimensional characteristics of the 5 MW NOW-WRSGs.

Initial Parameters	Value
Rated nominal power, Pt (MW)	5
Torque, T (kNm)	127
Synchronous speed, ns (r/min)	375 (16/18), 250 (24/27)
Rated frequency, fr (Hz)	50
Line voltage, VL (V)	400
Stator current, Is (A)	7500
Field current, If (A)	200
Number of rotor poles, p	16/24
Number of phases, m	3
Number of stator slots	18/27
Air gap, δ (mm)	5.5
Length of stack (mm)	1500
Outer diameter of stator (mm)	2120
Inner diameter of stator (mm)	1270

lists the conceptual specifications of the two machines; it is seen that the mechanical speed is operating at the medium-speed regime for wind generator applications. The three coils per phase are implemented for the double-layer winding of the 16/18 and 24/27 pole/slots combinations.

Before an evaluation of the radial forces can be conducted, some key winding parameters must be established. The machine is divided into sections that are repeatable to facilitate winding analysis. These machine sections, denoted as M_s, within the machine can be established by calculating the greatest common divisor, gcd, of the machine’s pole pairs p_p and the number of stator coils Q_s,

$$M_s=gcd\left(p_p,Q_s\right)$$

(1)

Similarly, the full stator winding can also be subdivided into sections that repeat. The windings sections, W_s, are calculated by determining the gcd of the total number of poles, p, and Q_s:

$$W_s=gcd\left(p,Q_s\right)$$

(2)

The number of machine and winding sections is then used to calculate the periodicity, τ, of the winding. Periodicity, which can be positive or negative, indicates the symmetry of the winding and is determined by

$$\tau ={\displaystyle \frac{M_s}{W_s}}$$

(3)

Positive periodicity occurs when τ = 1 and negative periodicity when τ = 2. The basic winding characteristics are listed in

Table 2. Winding parameters of the 5 MW NOW-WRSGs.

Initial Parameters	16/18	24/27
Machine sections	2	2
Winding sections	2	3
Periodicity	1	1
Number of coils in a phase	3	4
Working harmonic	4	4

.

The mathematical expression for the MMF in a traditional non-overlap winding with three phases comprising a set of coils can be expressed as follows:

$$F_{sv}={\displaystyle \frac{3\tau uN{k}_{wv}}{a\pi \left|v\right|}}I\mathrm{s}\mathrm{i}\mathrm{n}\left[\omega t-v\theta \right]$$

(4)

$$v=3\tau k+1, k\in Z,$$

(5)

where v denotes the number of the harmonic, u indicates the number of coils within a phase grouping, N represents the number of turns per phase, k_wv is the winding factor specific to the harmonic number, a represents the number of winding parallel paths, and I is the peak of the phase current. The winding factor k_wv is determined by the product of the pitch factor, k_pv, and distribution factor, k_dv. The MMF mathematical function for NOW, which considers the application of phase shifts between the coil currents of a phase group, was introduced in [10] and is outlined as follows:

$$F_{sv}={\displaystyle \frac{3N{k}_{pv}}{a\pi \left|v\right|}}{K}_{v}I\mathrm{s}\mathrm{i}\mathrm{n}\left(\omega t-v\theta -\beta \right),$$

(6)

where

$$K_v={\displaystyle \frac{\sqrt{{(1-\mathrm{c}\mathrm{o}\mathrm{s}b-\mathrm{c}\mathrm{o}\mathrm{s}c)}^2+{(\mathrm{s}\mathrm{i}\mathrm{n}c-\mathrm{s}\mathrm{i}\mathrm{n}b)}^2}}{u}}$$

(7)

$$b={\alpha }_2-v\theta$$

(8)

$$c={\alpha }_3-v\theta$$

(9)

and

$$\beta ={\tan }^{-1}\left({\displaystyle \frac{\sin c-\sin b}{1-\cos b-\cos c}}\right)$$

(10)

where θ is the electrical slot pitch angle, K_v is the new distribution factor of the winding, α₂ and α₃ are the phase displacements between the coils, and β represents the effect of the currents that are shifted in the phase. β = −30° is needed to result in increased performance of the machine while decreasing sub-harmonics in the MMF spectrum and is realized by creating a star-delta configuration between the set of coils of each phase group.

Figure 2 displays the MMF harmonic comparison between the 16/18 conventional NOW-WRSG, the 16/18 phase-shifted winding NOW-WRSG (PSW-WRSG) and the 24/27 NOW-WRSG. Note that multiples of the 3rd MMF harmonics of the stator do not exist in three-phase machines because the working or main harmonic is the 4th harmonic for a 16-pole and 24-pole configuration. The working harmonic is determined by the number of pole pairs per machine section. As elucidated previously in Table 2, the 16/18 configuration has two machine sections, while the 24/27 configuration has three machine sections. This yields the same working harmonics for the two models.

Note that the working harmonics of the 16/18 PSW-WRSG are higher than that of the 24/27 NOW-WRSG, based on the phase-shift theory of [10]. It is also important to highlight that although the 24/27 NOW-WRSG has higher sub-harmonics in general compared to the 16/18 PSW-WRSG, the former has a significantly smaller fifth harmonic even when compared to the 16/18 conventional NOW-WRSG. This is an indication of improved performance for higher pole count design, possibly due to the difference in flux path for the 5th harmonic in the two machines. The flux paths of the two machines at t = 100 ms are depicted in Figure 3. The PSW-WRSG shows higher flux concentration in certain areas compared to the 24/27 NOW-WRSG.

3. Electromagnetic Analysis and Structural Performance Comparison

3.1. Electromagnetic Performance Characteristics

The performance analysis is conducted with rated q-axis phase current and rated field current. The simulated torque curves for both machines are displayed in Figure 4 and the performance characteristics are summarised in

Table 3. Performance characteristics of the 5 MW NOW-WRSGs.

Initial Parameters	Value
	16/18 PSW-WRSG	24/27 NOW-WRSG
Output power, Pt [MW]	5.04	5.05
Voltage, VL [V]	400	400
Efficiency, η [%]	98.3	98.2
Core loss, PFe [kW]	22.71	19.4
Copper loss, PCu [kW]	59.32	64.82
Torque ripple, κδ [%]	5.2	5.7

. The resultant torque curves are comparable in terms of average torque and torque ripple, with only a slightly marginal difference. The impact of a higher number of poles is clearly seen by the number of cycles in the waveform.

The 24/27 pole/slot machine then exhibits lower core losses as indicated in Table 3. While the 16/18 machine exhibits lower 1st and 2nd harmonics compared to the 24/27 machine, the 5th harmonic of the 24/27 model is significantly reduced. The lower 5th harmonic of the 24/27 machine manifests as lower core losses [22]. As elucidated earlier in Figure 3, the shorter and less intense flux paths of the 24/27 machine confirm the reason for its reduced core losses. The flux density plots of the two models are displayed in Figure 5; a higher peak flux density is displayed in the rotor of the 24/27 machine due to higher MMF under the same field current.

The comparison of the 16/18 PSW-WRSG and the 24/27 NOW-WRSG shows a good correlation. Although both machines operate at different speeds, the aim of this part of the study is to ascertain the effect of the machine sections on the radial force distributions in the machines, since the same dimensions as well as electric and magnetic loading conditions are maintained.

Based on initial FEA electromagnetic performance analysis, the 24/27 NOW-WRSG shows comparable average torque and torque ripple. The lower core losses are attributed to the significantly reduced 5th harmonic in the MMF waveform, an indication of improved performance for the higher pole count design. The 16/18 PSW-WRSG still shows lower torque ripple, however, which is preferred for wind energy conversion systems. This is expected due to the lower 1st- and 2nd-order harmonics in the MMF spectrum compared to the 24/27 machine. The mechanical stress analysis will facilitate a better understanding of the difference in performance of these two machines.

3.2. Mechanical Stress Analysis

The mechanical stress analysis is performed via the radial force calculation technique by modelling the machines in terms of the flux distribution. Normally, the rotor’s surface experiences three directional force components because of the flux, namely radial, tangential and axial forces. However, the effect of the tangential force on the teeth is excluded from the assessment. While torque ripple influences machine vibrations, its primary impact is on the vibrations of the gearbox and as such, is excluded from this analysis. Therefore, the focus of this analysis is on assessing the effect of the different machine sections. The mechanical stress analysis is expected to reveal which NOW-WRSG pole/slot topology will result in a better balance of radial forces which translates to better fault tolerance.

To begin with, the magnetic field in the airgap can be described by

$$B_{sv}={\displaystyle \frac{{\mu }_0}{\delta k_C}}{F}_{sv},$$

(11)

where δ is the air gap length, and k_C is the Carter factor used for determining the effective air gap.

B_sv causes a pressure, P, which induces deflection in the stator and rotor iron. It is estimated using engineering beam theory and can be determined by [19]

$$P\left(t,\theta \right)={\displaystyle \frac{{B_{sv}}^2}{2{\mu }_0}}.$$

(12)

When calculating the radial force between the rotor and stator, the stator is modelled as a ring beam because the axial deflections can be ignored due to the rigidity of the stator teeth along the cylindrical axis. As such, the stator back iron carries the bending moment, and it can be estimated by

$$F_r={\displaystyle \frac{1}{2}}{\displaystyle \frac{B^2}{2{\mu }_0}}\delta l,$$

(13)

where l represents the length of the core in the axial direction.

The radial forces present in the machine, and the radial flux density component, B_radial, must be determined. This is achieved by determining the x and y components of the flux density vector simulated in FEA and converting them to cylindrical coordinates, i.e., radial and tangential components. The magnetic vibration in electric rotating machines is mainly due to the radial components.

The FEA-calculated radial flux densities at specific times around the air gap for the two machines are displayed in Figure 6. Figure 6a displays the radial flux density waveforms at t = 0.1 ms, while Figure 6b displays the radial flux density waveform at t = 100 ms. In both cases, it can be seen that the 16/18 PSW-WRSG exhibits higher peak amplitudes of radial flux density. Also, the peak-to-peak amplitude of the 16/18 PSW-WRSG is larger than that of the 24/27 NOW-WRSG.

The magnitude of the radial force for both machines is calculated as shown in Figure 7, at t = 100 ms. It is seen that the 16/18 machine experiences far greater radial forces and vibrations when compared to the 24/27 machine. The 16/18 with NOW winding has been included for comparison to illustrate the improvement as a result of the reduced MMF harmonics from the phase-shifted winding technique. The difference in amplitude of the radial forces from the 16/18 NOW to the 16/18 PSW is stark. This further verifies the advantage of the PSW applied to the WRSG, with an approximate 50% reduction in the radial forces. The 24/27 NOW-WRSG displayed significantly lower radial force compared to the 16/18 machine due to it having three machine sections as opposed to two for the 16/18 variant. With three equal sections, the airgap flux density waveform of the 24/27 machine had lower peak amplitudes and a smaller peak-to-peak variation since it can navigate a shorter flux path with a higher number of cycles. This resulted in reduced calculated radial forces based on Equation (13). Therefore, the three machine sections of the 24/27 design provide a better balancing of the radial forces acting around the airgap and will ultimately translate to improved structural performance and fault-tolerance capability for the machine. In practical terms, it means that the machine and the drive train will experience less wear and tear in the lifespan of the components. It must also be acknowledged that the radial forces present in the 16/18 machine have a predictable pattern and do not have a sinusoidal component. This means that although there are stronger forces present at certain places in the 16/18 NOW and PSW-WRSG machines, the fluctuation does not have a large 2nd-order nature which is typically responsible for bending and excessive audible noise [23].

4. Experimental Analysis

A prototype model of the 16/18 NOW-WRSG and 16/18 PSW-WRSG was built and tested in [10]. This study furthers the experimental analysis by analyzing the vibration of the machines. The prototype model is shown in Figure 8 and the specifications are listed in

Table 4. Parameters of the 3 kW 16/18 NOW-WRSG prototype machine [10].

Rated Parameters	Value
Rated power, Pt (kW)	3
Torque, T (Nm)	76.4
Synchronous speed, ns (r/min)	375
Frequency, f (Hz)	50
Line voltage, VL (V)	350
Stator current, Is (A)	4.86
Field current, If (A)	5
Number of poles, p	16
Number of phases, m	3
Number of stator slots	18
Air gap, δ (mm)	0.45
Length of stack (mm)	125
Outer diameter of stator (mm)	260
Inner diameter of stator (mm)	60
Output power, Pt (MW)	2.96

. Due to practical constraints, a prototype of the 24/27 NOW-WRSG could not be built and tested. However, the experimental data obtained assists in validating the theoretical FE models and gives confidence in the accuracy of the conclusions. The test setup for the experiment and the accelerometer placement are displayed in Figure 9. The vibrations were recorded following the process of [24]. The accelerometers are positioned on the front, with three similar units located on the back of the machine. These are PCB 333B32 accelerometers, connected to an HBM QuantumX MX1601B data acquisition system, all sourced from Tandm Technologies, Cape Town, South Africa.

The measured results of the vibration test are depicted in Figure 10. The results include the NOW and PSW windings applied to the same test machine. Low-frequency vibration is mainly of interest in engineering applications and therefore the electromagnetic vibration analysis is restricted to 1000 Hz for this application. The rotor remains the same and only the stator is changed. The measured data show a 50% reduction in acceleration amplitude between NOW and the PSW test machines. This verifies the theoretical finding that the 16/18 PSW-WRSG provides a reduction in radial forces and therefore machine vibration during operation. The results also support the finding that the 2nd-order or 100 Hz vibration component is not exceptionally large for these machines. The frequency modes are higher in the 800–1000 Hz range, but these modes are not easy to excite during operation.

5. Conclusions

In this study, electromagnetic and mechanical stress analysis is used to compare the performance of a 5 MW 16/18 pole/slots PSW-WRSG and a 24/27 pole/slots NOW-WRSG in FEA. The 24/27 machine showed comparable torque production but with lower core losses attributed to a significantly reduced 5th harmonic. The 24/27 machine exhibited significantly lower radial forces compared to the 16/18 variant due to possessing three as opposed to two machine sections. This results in better balancing of forces, which translates to improved structural integrity, vibration characteristics and fault-tolerance of the 24/27 pole/slots NOW-WRSG. The experimental results of the 16/18 pole/slot prototypes provide further insights into the benefits of the phase-shifted winding. The overall findings are important for establishing higher pole machines as viable solutions for wind generator applications. Modal analysis for calculation of the stator eigenfrequencies and vibrations and further optimization of the proposed machine designs will be undertaken in future for enhanced performance prediction.