I have been working on a project where so called Lundell alternator plays a crucial role. I haven't got any experience with this device sofar so I have decided to study some literature regarding this device at first. In the Power electronics handbook 3rd edition I have found on page 655 following equation describing alternator output power \$P_o = \frac{3\cdot V_o\cdot\sqrt{V_s^2-(4V_o^2/\pi^2)}}{\pi\omega L_s}\$, where \$V_o\$ is the battery voltage, \$V_s=k\omega i_f\$ is the back-emf voltage magnitude, \$\omega\$ is the electrical frequency and \$L_s\$ is the armature leakage inductance.
I have plotted a graph of the function \$P_o=P_o(V_o)\$ with following parameters \$L_s=135\,\mu H\$, \$k=9\cdot 10^{-3}\, V/(A\cdot rad\cdot s^{-1})\$, \$i_f=3.6\, A\$, \$n_m=3000\,min^{-1}\$ (mechanical speed of the combustion engine), \$p=3\$ (number of alternator pole pairs).
From the graph it seems that the alternator power function has "interesting" behavior only for unrealizable (at least in standard vehicle with 12 V lead-acid battery) voltages. Does anybody have any suggestion what could be the main idea behind this function? Thanks for any suggestions.
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