Question

A three-phase, 230 v, 80 kva, 0.9 pf (lagging) load is supplied by three 32 kva, 1330/230 v, 60 hz transformers connected in by means of a common three-phase feeder with an impedance of 0.003 j0.015 ohms per phase. the transformers are supplied from a three-phase source (substation) through a three-phase line with an impedance of 0.95 j4.6 ohms per phase. the equivalent impedance of one or the single-phase transformers referred to the low-voltage side is 0.18 j0.3 ohms.

(a) determine the required supply voltage if the load voltage is 230 v.
(b) determine the voltage regulation.

Answer 1

The required supply voltage is calculated using the formula for voltage regulation. The voltage regulation is found to be 173.2%. The voltage regulation is also calculated using the given values for full-load impedance, transformer impedance, and short circuit impedance. The calculated voltage regulation is 3.71%.

Step-by-step explanation:

(a) To determine the required supply voltage if the load voltage is 230 V, we need to calculate the voltage regulation. Voltage regulation is given by the formula:

Vreg = (Vnl - Vfl) / Vfl * 100%

Where:

Vreg is the voltage regulation

Vnl is the no-load voltage

Vfl is the full-load voltage

Given that the no-load voltage is 1.732 * 230 V (because it is a three-phase system) and the full-load voltage is 230 V, we can substitute these values into the formula:

Vreg = (1.732 * 230 - 230) / 230 * 100%

After calculating this expression, we find that the voltage regulation is 173.2%.

(b) To determine the voltage regulation, we can use the formula:

% Vreg = (Zfl / Zfl + Ztr + Zsc) * 100%

Where:

% Vreg is the percentage voltage regulation

Zfl is the full-load impedance

Ztr is the transformer impedance

Zsc is the short circuit impedance

Substituting the given values, we get:

% Vreg = (0.18 + 0.003 + 0.003) / (0.18 + 0.003 + 0.003 + 0.015 + 0.95 + 4.6) * 100%

Simplifying this expression, we find that the voltage regulation is 3.71%.