(Solved): Q2. (a) The load taken from a single-phase ac supply consists of: (i) a resistive heating load ...

Q2. (a) The load taken from a single-phase ac supply consists of: (i) a resistive heating load of $40\mathrm{kW}$; (ii) a motor load of $40\mathrm{kVA}$ at 0.65 power factor lagging; and (iii) a load of $30\mathrm{kW}$ at 0.9 power factor lagging. Calculate the total load on the supply in KW and kVA and its power factor. $[10$ marks] (b) A single-phase $50\mathrm{kW}$ industrial load operates from a $1\mathrm{kV}$ (rms), 50 Hz supply with a power factor of 0.6 lagging, as shown in Figure 2.1 . The industrial plant owner needs to raise the power factor of the load to 0.9 lagging or above in order to avoid additional charges from the electricity supplier. Power factor correction capacitors can be purchased as follows: (i) $33?\mathrm{F}$ capacitors at a cost of 695 per unit; or (ii) $69?\mathrm{F}$ capacitors at a cost of $€175$ per unit. Determine the number and type of capacitors to be purchased in order to achieve the desired power factor correction at the minimum cost. [10 marks]