Elementary electric machine Solution

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EXERCISES FOR ELECTRIC POWER SYSTEMS COURSE ENERGY DEPARTMENT, Electrical section 1 Class 2 - solution Elementary electric machine Description of the machine’s operating conditions : Steady-state operation of the elementary electric machine (EEM) Let us consider the electrical circuit of the EEM supplied by the voltage source V representing the external network as depicted in the following Figure The current I is driven by the voltage source V and, due to the mechanical action of the magnetic field ( B) on the mobile part, an electrodynamic force /g1832 /g3532/g3531 acts on the mobile part. The electrodynamic force direction is given by the left – hand rule : and its expression by /g1832/g3532/g3531 /g3858 /g1828/g1836/g1833 Therefore Force /g1832 /g3532/g3531 will determine the mobile part to move along the fixed part. For stable steady-state operation of the machine it is necessary for the mobile part to move along the fix part with constant velocity ( v). For this, the /g1832/g3532/g3531 needs to be balanced by a mechanical load /g1832/g3585. Considering also the frictional forces between the mobile and the fix parts, we have S d x B I RV S d x B I R V Fed EXERCISES FOR ELECTRIC POWER SYSTEMS COURSE ENERGY DEPARTMENT, Electrical section 2 and /g1832/g3585/g3367/g1832/g3533/g3583/g3858/g1832/g3532/g3531 /g3858 /g1828/g1836/g1833 (A) /g1878/g3858 /g1833/g1867/g1866/g1871/g1872 (B) Moreover, due to the movement of the mobile part, the area defined by the fixed and mobile parts (rectangle xd in the above figure) increases and thus, the magnetic flux crossing it increases in time according to /g2538/g8666/g1872/g8667/g3858 /g1828 ∙ /g1836 ∙ /g1876/g8666/g1872/g8667. Therefore, an emf is induced in the electric circuit. Assuming the velocity of the mobile part constant (…