Question

Consider a single-phase circuit where a 14 kV, 60 Hz voltage source feeds an electric load through a feeder whose impedance is 1.5 + j 3 Ω. The load is known to consume 4 MW and 3 MVAR. Let V and δ represent the rms voltage and its phase angle (relative to the source voltage) at the load terminals. Two equations are needed to solve for V and δ. 1) Derive two analytical expressions in terms of V and δ that need to be solved. Determine the values of V and δ (hint: numerical solution is required) Determine the active and reactive powers supplied by the source. 2) 3)

Answer 1

Given rightarrow consider a single phase circuit having * voltage (*v) = 14 kv * and frequency = 60 HZ * impedance = 1.5 + j 3 Ohm * the load is consume 4 MW and 3 MVAR let us assume v = rms voltage 8 = phase voltage (a) derivation of two analytical expressions in terms of v and s: now power factor = cos [Tan^-1 (3/4)] = cos [36.8698] = 4/5 power factor = 0.8 [lagging] \r\n p = v_l I_l cos theta implies I_l = p/v_l cos theta therefore p = 4 MW = 4 times 10^6 m and cos theta = 0.8 implies I_l = 4 times 10^6/V_l times 0.8 implies I_l = 5 times 10^6/v_l A and 14 times 10^3 - 5 times 10^6/v_l angle -36.87 (1.5 + j 3) = v_l angle 5 implies 14 times 10^3 - [4 times 10^6 - j 3 times 10^6/v_l] (1.5 + j 3)