Poynting Theorem Applied to Cable Wound Generators

Power flow in the air gap of linear electrical machines by utilization of the Poynting vector: Part 1 ‐ Analytical expressions

“…Inspired by Maxwell's ”Treatise on electricity and magnetism” [1, 2], Poynting derived a theorem describing how the power flux is connected to the electric and magnetic fields: $$\begin{equation} \vec{S} = \vec{E} \times \vec{H}, \end{equation}$$where $$\vec{S}$$ is Poynting's vector, $$\vec{E}$$ is the electrical field, and $$\vec{H}$$ is the magnetic field strength. This is now referred to as Poynting's theorem, which is useful, among other things, when analyzing the power flow in an electrical machine [3–9]. For example, Chebak et al.…”

“…Another example is Bolund et al. [7], who made a detailed study of the power flow in the cables in a cable wound generator by simulating the Poynting vector.…”

“…When the Poynting vector has been used to understand electrical machines, it has almost exclusively been done for rotating electrical machines [3–8]. The authors have found one study on linear electrical machines where the Poynting vector is used, made by Dang et al.…”

“…where ⃗ S is Poynting's vector, ⃗ E is the electrical field, and ⃗ H is the magnetic field strength. This is now referred to as Poynting's theorem, which is useful, among other things, when analyzing the power flow in an electrical machine [3][4][5][6][7][8][9]. For example, Chebak et al [8] used a method from [10] to find the eddy current losses in the stator from Poynting's vector.…”

Eddy Current Losses in Solid Pole Shoes in a Two-Pole Permanent Magnet Motor

“…The choice to work with cable winding is done with the physical background of Maxwell and Poynting in mind. B. Bolund [13] present detailed studies of the electric field distribution on different shapes of conductors, all with strongly benefits of the circular design, where the distribution of the electrical field is smooth, without hot spots which can be seen in, for example in the corner within a rectangular winding. The dimension is set by the voltage and power rating of the motor, where the number of slots per pole and phase, cables per slot and the magnetic circuit is designed with high efficiency and the total weight in mind.…”