Answer:
(i):
R_eq ≈ 2777.78 ohms
X_eq = 10 ohms
X_m ≈ 1666.67 ohms
(ii):
N = 1/5
3000 VA = 200 V * (5 * I_secondary)
V_secondary ≈ -8133.34 V - j30 V
Final:
The percentage regulation is approximately 100%
Step-by-step explanation:
To find the parameters of the equivalent circuit referred to the low-voltage (LV) side, you can use the open-circuit (O.C.) and short-circuit (S.C.) test results.
(i) Parameters of the Equivalent Circuit Referred to the LV Side:
1. Equivalent Resistance (R_eq):
Use the O.C. test results:
Voltage (V_oc) = 2000 V
Current (I_oc) = 1.2 A
Power (P_oc) = 90 W
R_eq = (V_oc / I_oc)^2 / P_oc
R_eq = (2000 V / 1.2 A)^2 / 90 W
R_eq ≈ 2777.78 ohms
2. Equivalent Reactance (X_eq):
Use the S.C. test results:
Voltage (V_sc) = 50 V
Current (I_sc) = 5 A
Power (P_sc) = 110 W
X_eq = V_sc / I_sc
X_eq = 50 V / 5 A
X_eq = 10 ohms
3. Magnetizing Reactance (X_m):
X_m can be found using the O.C. test results:
X_m = V_oc / I_oc
X_m = 2000 V / 1.2 A
X_m ≈ 1666.67 ohms
(ii) To calculate the output secondary voltage when delivering 3 kW at 0.8 power factor (lagging), you can use the following formula for the apparent power (S):
S = V_primary * I_primary = V_secondary * I_secondary
Given:
- Input primary voltage (V_primary) = 200 V
- Output power (P_out) = 3 kW (3000 VA)
- Power factor (PF) = 0.8 (lagging)
First, calculate the output current (I_secondary):
P_out = V_secondary * I_secondary * PF
I_secondary = P_out / (V_secondary * PF)
I_secondary = 3000 VA / (V_secondary * 0.8)
Next, calculate the current on the primary side (I_primary) using the turns ratio (N):
N = V_primary / V_secondary
I_primary = I_secondary / N
Now, calculate N:
N = V_primary / V_secondary
N = 200 V / 1000 V
N = 1/5
I_primary = I_secondary / (1/5)
I_primary = 5 * I_secondary
Now, you can calculate I_primary:
I_primary = 5 * I_secondary
Substitute this into the equation for apparent power (S):
S = V_primary * I_primary
3000 VA = 200 V * (5 * I_secondary)
Solve for I_secondary:
I_secondary = 3000 VA / (200 V * 5) = 3 A
Now that you have I_secondary, you can find the secondary voltage (V_secondary) using the formula:
V_secondary = V_primary - (I_secondary * (R_eq + jX_eq))
V_secondary = 200 V - (3 A * (2777.78 ohms + j10 ohms))
V_secondary ≈ 200 V - (8333.34 ohms + j30 ohms)
V_secondary ≈ 200 V - (8333.34 ohms + j30 ohms)
V_secondary ≈ 200 V - 8333.34 ohms - j30 ohms
V_secondary ≈ (200 V - 8333.34 ohms) - j30 ohms
V_secondary ≈ -8133.34 V - j30 V
Now, to find the percentage regulation, use the formula:
Percentage Regulation = ((V_no_load - V_full_load) / V_full_load) * 100%
V_no_load is the no-load secondary voltage, and V_full_load is the calculated secondary voltage when delivering 3 kW.
Percentage Regulation = ((-8133.34 V - 0 V) / -8133.34 V) * 100%
Percentage Regulation ≈ (8133.34 V / 8133.34 V) * 100%
Percentage Regulation ≈ 100%
The percentage regulation is approximately 100%.