A 220 V 1400 rpm, 40 A separately excited dc motor has an

A 220 V 1400 rpm, 40 A separately excited dc motor has an armature resistance of 0.4Ω. The motor is fed from a single phase circulating current dual converter with an input ac line voltage of 220 V (rms). The approximate firing angles of the dual converter for motoring operation at 50% of rated torque and 1000 rpm will be

At rated speed and torque, E = V – I_a R_a= 220 – 40 × 0.4 = 204 volts
At 1000 rpm and 50% of rated torque, since
T ∝ I

I₂ =	1	× 40 = 20 A
	2

∴ E₂ =	E₁	× N₂
	N₁

=	204	× 1000 = 145.71 volts
	1400

∴ Applied Voltage, V₂ = E₂ + I ₂ R₂
= 145.71 + 20 × 0.4 = 153.71 volts
Hence output of converter (rectifier 1),

V₀ =	2V_m	cos α₁ = 153.71
	π

∴	2 × √2 × 220	cos α₁ = 153.71
	π

⇒ α₁ = 39.1° ≈ 39°
∴ Firing angle of rectifier, α₂ = 180 – α₁ = 141°
Hence α₁ = 39° and α₂ = 141°