# Design procedure of coreless stator PM axial field synchronous machine for small-scale wind applications

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## Abstract

Axial field machines are available in a wide range of configurations. It has flexible design restrictions. Several research efforts were performed to discover machine performance and design horizons. However, the common design process of axial field machines depends on numerical field analysis, due to the lack of trusted and generalized analytical and/or empirical formulas especially for field distribution. This paper aims to present the essential analytic formulation for dimension selection. In addition, it provides the normalized relations between dimensions and airgap flux density using 3D-FEM as an alternative for empirical formulas. The paper describes a design procedure for coreless stator axial flux permanent magnet synchronous machine. Definite equations are derived to help the designer select the proper number of PM poles and concentrated coils to get balanced multi-phase voltage out of the generator. Moreover, the paper defines the necessary limitations of the span of the concentrated coil for a certain pole pitch to reduce the harmonic content of the output voltage waveform. The paper proposes a new approach for selecting the dimensions of the magnetic circuit using proposed data curves instead of struggling with the 3D-FEM along with its high time consumption and the need for high computational power. The loss calculations and the armature reaction are also investigated as a performance analysis criteria for the designed generator. The paper investigates the design for small-scale wind applications. The design procedure is validated using both 3D-FEM simulations and experimental results. The results show the consistency of the proposed procedure. The procedure is described and applied for a certain configuration and materials. However, it is solely extendable to several other configurations.

## Keywords

Finite element analysis Generators Permanent magnet machines## List of symbols

- \(e_{\mathrm{cond}}\)
Induced voltage in a single conductor (V)

- \(e_{\mathrm{coil}}\)
Induced voltage in a single coil (V)

- \(e_{\mathrm{ph}}\)
Induced voltage per phase (V)

- \(E_{\mathrm{ph}}\)
RMS-induced voltage per phase (V)

- \(v_{\mathrm{ph}}\)
Stator terminal voltage per phase (V)

- \(B_{\mathrm{ag}}\)
Average flux density in the airgap (T)

- \(l_{\mathrm{cond}}\)
Active length of the conductor (m)

- \(\omega _{\mathrm{m}}\)
Angular speed of the rotor (rad/s)

- \(N_{\mathrm{rpm}}\)
Speed of the rotor (r/min)

- \(r_{\mathrm{m}}\)
Mean radius of the rotor disc (m)

- \(T_{\mathrm{coil}}\)
Number of turns in each coil

*q*Number of coils per phase

- \(P_{\mathrm{in}}\)
Input power (kW)

- \(P_{\mathrm{o}}\)
Output power (kW)

*T*Developed torque (Nm)

*m*Number of phases

- cos(\(\phi \))
Power factor

- \(i_{\mathrm{ph}}\)
Induced current per phase (A)

- \(\eta \)
Machine overall efficiency

- \(D_{\mathrm{in}}\)
Inner diameter of rotor disc (m)

- \(D_{\mathrm{o}}\)
Outer diameter of rotor disc (m)

- \(r_{\mathrm{i}}\)
Inner radius of rotor disc (m)

- \(r_{\mathrm{o}}\)
Outer radius of rotor disc (m)

- \(\tau \)
Pole arc-to-pole pitch ratio

- \(\delta \)
Current density in stator winding (\(\hbox {A/m}^{2}\))

- \(a_{\mathrm{c}}\)
Cross-sectional area of stator conductor (\(\hbox {m}^{2}\))

- \(l_{\mathrm{tot}}\)
Total length of stator conductors (m)

- \(N_{\mathrm{c}}\)
Number of stator coils

*p*Number of PM poles

- \(h_{\mathrm{m}}\)
Magnet height (mm)

- \(l_{\mathrm{m}}\)
Magnet length (mm)

- \(w_{\mathrm{m}}\)
Magnet width (mm)

- \(h_{\mathrm{y}}\)
Height of rotor yoke (mm)

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