Test: Per Unit System - Electrical Engineering (EE) MCQ

Per Unit System:

• The per-unit value of any quantity is defined as the ratio of actual value in any unit to the base or reference value in the same unit.
• Any quantity is converted into per unit quantity by dividing the numeral value by the chosen base value of the same dimension. The per-unit value is dimensionless.
   

PU Value (PU) = A/B

Here, A is the actual value in any unit
B is the Base or reference value in the same unit

Consider the base value of voltage is (kV_B), the Base value of current is (I_B) and the base value of apparent power is (kVA_B)
And, Base value of current (I_B)
Now, the Base value of the impedance (ZB) will be the ratio of the base value of voltage to the current.

From equation (1),

Hence, per unit value of impedance can be written as if Z is the actual value of impedance,

Since the above expression is given infraction of 1000 units,
Hence per unit value will be given as,

Calculation:

We have,

kV_B = 10 kV,

MVA_B = 10 MVA

Hence,

Z_B = 10²/10 = 10 ohms

Concept:

Per unit quantity:

Per unit quantity = Actual quantity in the units / Base (or) reference quantity in the same units

⇒ Per unit impedance Z_pu = Z_actual / Z_base

⇒ Z_pu = Z_Ω × MVA_b / (kV_b)²

Conversion of one per unit impedance into another per unit impedance is given by

Calculation:

Let's consider

Z_pu old = x

MVA_old = M

kVb _old = V

As base kV and base MVA are both doubled

MVA_new = 2M

kVb _new = 2V

⇒ X_pu(new) = x × (2M / M) × (V / 2V)² = x/2 p.u

Concept:

The relation between new per-unit value & old per unit value impedance


Where,

(Z_pu)new = New per unit value of impedance

(Z_pu)old = Old per unit value of impedance

kV_base = Old base value of voltage

kV_new = New base value of voltage

MVA_new = New base value of power

MVA_old = Old base value of power

Calculation:

Given that,

X_old = 0.25 PU

MVA_old = 500 MVA

KV_old = 18 kV

MVA_new = 100 MVA

KV_new = 20 kV

Concept:

Per unit quantity:

Per unit quantity = Actual quantity in the units / Base (or) reference quantity in the same units

⇒ Per unit impedance Z_pu = Z_actual / Z_base

⇒ Z_pu = Z_Ω × MVA_b / (kV_b)²

Conversion of one per unit impedance into another per unit impedance is given by

Calculation:

Given that

Z_pu old = 0.2

MVAold = 100 MVA

kVb _old = 132 kV

MVA_new = 50 MVA

kVb _new = 220 kV

A long transmission line under no-load conditions behaves as the capacitive load. The effect of armature current is purely magnetization. When the alternator is disconnected, there is no magnetizing effect. So the terminal voltage decreases with the same field current.

Explanation:

When the generator is connected to an open-circuit transmission line, the line draws a charging current, therefore V_t > E_g.

But, when the generator is disconnected from the line, no charging current is delivered by the generator, i.e.,

I_c = 0 ⇒ V_t = E_g.

So, the terminal voltage decreases.

25 MVA, 33 kV transformer – Z_{pu old} = 0.9, MVA_old = 25 MVA, V_old = 33 kV

At new base, P_new = 50 MVA, V_new = 11kV

As Z_pu = Z/Z_base

= 0.9 × 2 × 9

Z_{pu new} = 16.2 pu

Concept:

Where kV_old = old base value of voltage,

kV_new = New base value of voltage,

MVA_old = Old base value of machine rating,

MVA_new = New base value of machine rating,

Calculation:

Per unit value of a quantity is defined as the ratio of its actual value to its base value.

Per unit impedance = actual impedance / base impedance

Important Point:

The relation between new per-unit value & old per unit value impedance


Where,

(Z_pu)_new = New per unit value of impedance

(Z_pu)_old = Old per unit value of impedance

kV_base = Old base value of voltage

kV_new = New base value of voltage

MVA_new = New base value of power

MVA_old = Old base value of power

Per unit quantity:

Per unit quantity = Actual quantity in the units / Base (or) reference quantity in the same units

⇒ Per unit impedance Z_pu = Z_actual / Z_base

⇒ Z_pu = Z_Ω × MVA_b / (kV_b)²

Conversion of one per unit impedance into another per unit impedance is given by

V = 0.9 pu. and cos ϕ = 0.8 lag.

Base power = 100 MVA

Base current = 437.38 A

P.U. value = Actual value / base value

Now, the base

 

Now, V_actual = 0.9 pu × 132 kV

⇒ V_actual = 118.8 kV

⇒ V_L−L = V_actual

V_L-L = 118.80 kV

Given that, pu parameters for a 300 MVA machine on its own base Inertia: M_old = 10 pu

Reactance: X_old = 4 pu

New base = 50 MVA

New pu value of inertia,

New pu value of reactance,


Note:

We know that Pu value depends on the base value of that quantity hence the actual value of that quantity is always equal-

pu value old = actual/old base

Now, new pu value = actual/new base

⇒ Pu_old × Base old = Pu_new × Base_new

⇒ pu new = (pu old × old base)/(new base) 

Concept:

The relation between new per-unit value & old per unit value impedance


Where,

(Z_pu)new = New per unit value of impedance

(Z_pu)old = Old per unit value of impedance

kV_base = Old base value of voltage

kV_new = New base value of voltage

MVA_new = New base value of power

MVA_old = Old base value of power

Calculation:

Given that,

X_d(old) = 0.2 pu

MVA_(new) = 100

MVA_(old) = 500

KV_(old) = 11

KV_(new) = 22

Concept:

The relation between new per-unit value & old per unit value impedance


Where,

(Z_pu)new = New per unit value of impedance

(Z_pu)old = Old per unit value of impedance

kV_base = Old base value of voltage

kV_new = New base value of voltage

MVA_new = New base value of power

MVA_old = Old base value of power

Calculation:

Given that,

X_d(old) = 1 pu

MVA_(new) = 200

MVA_(old) = 100

kV_(old) = 20

kV_(new) = 20

Formula:

For an AC network,

VA Rating = V²/Z

Where V is voltage in volt

Z is the impedance (base) in Ω

Application:

VA rating = 40 MVA = 40 × 10⁶ VA

V = 14.6× 10³ volts

From above formula,

Alternate Method:
Since,

(kilo)² = Mega

Therefore the formula for base impedance is also written as,

Per unit (p.u.) quantity:

The per-unit value of any quantity is defined as the ratio of actual value in any unit to the base or reference value in the same unit.

The per-unit value is dimensionless.

​Per unit impedance (Z_pu):

Z_pu is defined as the ratio of actual value to base impedance.

It is also defined as The ratio of full-load volt-amperes to short-circuit volt-amperes.

Z_a = Actual impedance

Z_B = Base impedance

(kVA)_B = Base kVA

(kV)_B = Base voltage in kV

Important points:

• Per unit voltage (V_pu) = (kV)_actual / (kV)_B
• Short circuit current in pu = Actual current / Base current