Voltage Regulation MCQ Quiz - Objective Question with Answer for Voltage Regulation - Download Free PDF

Concept

The voltage drop per phase (in V/phase) is given by:

V = I × Z_T

where, V = Voltage drop

I = Current

Z_T = Total Impedance

Calculation

Given, cosϕ = 0.8 lag → ϕ = 36.86° 

I = 50∠-36.86° 

Length = 400 m = 0.4 km

Z_T = (0.15 + j0.2) × 0.4

ZT = (0.06 + j0.08) Ω/km

V = (50∠-36.86°) × (0.06 + j0.08)

V = 50(0.8 - j0.6) × (0.06 + j0.08)

V = (40 - j30) × (0.06 + j0.08)

V = 4.8 + j1.4

Explanation:

Voltage Regulation of a Transmission Line

Problem Statement:

A single-phase 60 Hz generator supplies an inductive load of 4500 kW at a power factor of 0.80 lagging through a 20 km long overhead transmission line. The line resistance and inductance are 0.0195 ohm and 0.60 mH per km, respectively. The voltage at the receiving end is required to be maintained at 10.2 kV. The task is to calculate the voltage regulation of the line.

Given Data:

• Power (P): 4500 kW = 4500 × 10³ W
• Power factor (pf): 0.80 (lagging)
• Receiving end voltage (V_R): 10.2 kV = 10.2 × 10³ V
• Line length (L): 20 km
• Resistance per km (R/km): 0.0195 Ω
• Inductance per km (L/km): 0.60 mH = 0.60 × 10^-3 H
• Frequency (f): 60 Hz

Step-by-Step Solution:

Step 1: Calculate the receiving end current (I_R)

The apparent power (S) is related to the real power (P) and power factor (pf) as:

S = P / pf

Substituting the values:

S = (4500 × 10³) / 0.80 = 5625 × 10³ VA = 5625 kVA

The current (I_R) is given by:

I_R = S / (√2 × V_R)

Substituting the values:

I_R = (5625 × 10³) / (√2 ×10.2 ×10³)

Concept

The receiving end voltage of a single-phase short transmission line is given by:

\(V_R=V_S-I_R(R+jX)\)

where, V_R = Receiving end voltage

V_S = Sending end voltage

I_R = Receiving end current

R = Resistance

X = Inductive Reactance

Calculation

Given, VS = 1.1 kV = 1100 kV

IR = 50 ∠-36.86° 

R = 4 Ω 

X = 6 Ω 

\(V_R=1100-(50\angle-36.86)(4+j6)\)

\(V_R=1100-(50\angle-36.86)(7.74\angle 56.30)\)

\(V_R=1100-(387.29\angle 19.44)\)

\(V_R=734.78\space +\space j128.89\)

VR = 760 V

Line regulation for short transmission lines specifically measures how much voltage drop occurs along the length of the transmission line, making it a critical factor in assessing the performance of electrical transmission systems.
​
Explanation:

• Line Regulation: Line regulation refers to the ability of a transmission line to maintain a constant voltage level at the receiving end despite variations in load current. It indicates how much the voltage changes as the load on the line changes.
• Voltage Drop: In short transmission lines, the voltage drop is primarily caused by the resistance and reactance of the line. As the load increases, the current through the line increases, resulting in a greater voltage drop along the length of the line. Line regulation quantifies this drop.
• Importance of Line Regulation: Good line regulation is crucial for ensuring that consumers receive a stable voltage level, which is essential for the proper functioning of electrical equipment.

Concept of Voltage Regulation and Power Factor:

Voltage regulation (VR) is defined as the difference between the sending end voltage (V_S) and the receiving end voltage (V_R), expressed as a fraction of the receiving end voltage:

VR = (V_S - V_R) / V_R

For a leading power factor load, the voltage regulation can be affected by the inductive reactance (X_L) and the line resistance (R) of the transmission line. The expression for voltage regulation in terms of these parameters is:

VR = (I R cosϕ_R) - (I X_L sinϕ_R)

Where,

• I = Line Current
• R = Line Resistance
• X_L = Line Reactance
• V_R = Receiving End Voltage
• cosϕ_R = Load Power Factor (leading)
   

Given Condition:

• The receiving end voltage (V_R) is more than the sending end voltage (V_S), indicating a leading load power factor. This condition implies that the reactive component is capacitive, causing the voltage to rise.
• In a transmission line with a leading power factor, the voltage regulation is negative, meaning the receiving end voltage (VR) is higher than the sending end voltage. The leading power factor causes the capacitive reactance to dominate, which means the reactive component (IXL) plays a larger role than the resistive component (IR). This leads to the condition where IR COSϕR is less than IXLCOSϕR.
   

Correct Expression for Leading Power Factor: IR cosϕ_R < I X_L cosϕ_R

Conclusion:

Hence, the correct expression for the leading load power factor is:

IR cosϕ_R < I X_L cosϕ_R

Concept:

Voltage regulation of Transmission line:​

• When a transmission line is carrying a current, there is a voltage drop in the line due to the resistance and inductance of the transmission line.
• Finally, the receiving end voltage ( VR ) of the line is generally less than the sending end voltage (VS)
• The difference in voltage at the receiving end of the transmission line between the conditions of no-load and the full load is called voltage regulation
• Voltage regulation is expressed as a percentage of the receiving end voltage.

 \(V.R =\frac{V_S - V_R}{V_R} \times 100=\frac{{\left| {V_R^{NL}} \right| - \left| {{\rm{V}}_{\rm{R}}^{{\rm{FL}}}} \right|}}{{\left| {{\rm{V}}_{\rm{R}}^{{\rm{FL}}}} \right|}} \times 100\)

Note: At no load, \(|V_S|=|V_R|\)

The correct answer is option 2):((a) and (b) only)

Concept:

• A feeder is a conductor having constant current density. The size of the feeder is designed based on current-carrying capacity. For V ≤ 220 kV, the selection of conductor is done based on the current-carrying capacity.
• The main criteria for the design of a feeder are its current carrying capacity which accounts for thermal limits rather than voltage drops.
• A distributor has variable loading along its length due to the service conditions of tapping by the individual consumers. The voltage variation at the consumer end must be kept under ±5%. So, the main criterion for the design of a distribution feeder is voltage regulation or voltage drop.
• Hence c) Voltage variation at the consumer's terminal is not considered while designing the distributor is wrong

Concept:

Voltage regulation of the transmission line is defined as the ratio of the difference between sending and receiving end voltage to receiving end voltage of a transmission line between conditions of no-load and full load.

It can be expressed in percentage as

\(V.R = \frac{{{V_{RN}} - {V_{RF}}}}{{{V_{RF}}}} \times 100\)

Sending end voltage for the transmission line is given as,

V_S =AV_r + BI_r

Under no-load condition, Ir = 0

Calculation:

Voltage at sending-end,

V_s = AV_R + BI_R

At no-load, I_R = 0

From the given data,

V_RF = 220 kV

From the above concept,

\(\begin{array}{l} \Rightarrow {V_{RN}} = \frac{{{V_S}}}{A} = \frac{{240 \times {{10}^3}}}{{0.94}} = 255.3kV\\ \% \ V.R = \frac{{255.3 - 220}}{{220}} \times 100 = 16\% \end{array}\)

Concept:

Voltage regulation of transmission line is defined as the ratio of the difference between sending and receiving end voltage to receiving end voltage of a transmission line between conditions of no-load and full load.

It can be expressed in percentage as

\(\% VR = \frac{{{V_s} - {V_R}}}{{{V_R}}} \times 100\)

Where Vs is the sending end voltage per phase and VR is the receiving end voltage per phase.

Percent regulation, \(= \frac{{IRcos{\phi _r} \pm IXsin{\phi _r}}}{{{V_r}}} \times 100\;\)

Application:

Maximum regulation occurs at lagging power factor only

\(\frac{d}{{d\phi }}\left( {R\cos \phi + X\sin \phi } \right) = 0\)

\( \Rightarrow \tan \phi = \frac{X}{R}\)

Additional Information

Zero regulation occurs at leading power factor only

\(\Rightarrow \frac{{IRcos{\phi _r} - IXsin{\phi _r}}}{{{V_r}}} \times 100 = 0\;\)

\(\Rightarrow IRcos{\phi _r} = IXsin{\phi _r}\)

The correct answer is option 1): (0.707 leading)

Concept:

• In a short transmission line, the length of the line is below 80 km, and the line voltage is comparatively low (below 69 kV). Hence the capacitance effects of the line are extremely small and thus neglected.
• Voltage regulation = \(= \frac{{IRcos{\phi _r} \pm IXsin{\phi _r}}}{{{V_r}}} \times 100\;\)

For zero voltage regulation,

IV(Rcos⁡ϕ−Xsin⁡ϕ) = 0 (leading power factor)

⇒ tan ϕ = \( R\over X\) If R = X,

then tan ϕ = 1 ⇒ ϕ = 45°

Power factor, cos ϕ = cos 45°= 0.707 leading power factor​

The correct answer is option 2):(25.2 V)

Concept:

The percentage regulation is defined as:

\(\%~R = \frac{{({V_{NL}} - {V_{FL}})}}{{{V_{FL}}}}\times\;100\;\%\)

V_NL = No load voltage

V_FL = Full load voltage

Calculation:

\(\frac{5}{{100}} = \frac{{({V_{NL}} - 24)}}{{24}}\)

\(\frac{5}{{100}}.\left( {24} \right) = ({V_{NL}} - 24)\)

Condition for Zero and Maximum Voltage Regulation

• Voltage regulation is a measure of the change in the voltage magnitude between the sending and receiving end of a component from no load to full load as a percentage of full load voltage.
• During the calculation of voltage regulation, we only deal with the magnitude of quantities not along with phasor.

Voltage regulation is given by this approximation 

V.R. = \(\rm \left(\frac{I_R}{V_R}\right)[R\cos ϕ_R\pm X \sin ϕ_R]\)

V.R. = \(\rm \left(\frac{I_R}{V_R}\right)\times\sqrt{R^2+X^2}\left[\frac{R}{\sqrt{R^2+X^2}}\cosϕ_R\pm \frac{X}{\sqrt{R^2+X^2}}\sin ϕ_R\right]\)

\(\rm \cos θ=\frac{R}{\sqrt{R^2+X^2}}\) and \(\rm \sin θ=\frac{X}{\sqrt{R^2+X^2}}\)

\(\rm \tanθ=\frac{X}{R}\)

\(\rm Z_{eq}(pu)=\frac{\sqrt{R^2+X^2}}{\left(\frac{V_R}{I_R}\right)}\)

V.R. = Z_eq(pu) cos (θ - ϕ_R) → for lagging loads

V.R. = Zeq(pu) cos (θ + ϕR) → for leading loads

Condition for Zero Voltage Regulation

• Zero voltage regulation means, Sending end voltage and Receiving end voltage become equal.
• This case is also known as the ideal voltage regulation. Ideal voltage regulation is desirable in a power system but not possible practically.
• Zero voltage regulation can only be achieved when the nature of the load is of leading.

⇒ V.R. = 0 ⇒ At leading loads

V.R. = Z_eq(pu) cos (θ + ϕ_R)

Zeq(pu) cos (θ + ϕR) = 0

cos (θ + ϕR) = 0

(θ + ϕR) = 90°

ϕ_R = 90° - θ

cos ϕ_R = cos (90° - θ) = sin θ

\(\rm \sin θ =\frac{X}{\sqrt{R^2+X^2}}\)

Value of the receiving end power factor in order to achieve the zero voltage regulation is given below:

⇒ \(\rm \cosϕ_R =\frac{X}{\sqrt{R^2+X^2}}\) (Leading load)

Condition for Maximum Voltage Regulation

• Maximum voltage regulation means the difference between the receiving end voltage and the sending end becomes very large and such a case can only happen when the nature of the load is of lagging.
• The expression of voltage regulation for a lagging load is given below:

V.R. = Z_eq(pu) cos (θ - ϕ_R)

The maximum value of cosine function occurs when its argument becomes equal to 0°

cos (θ - ϕ_R) = 1

θ - ϕR​ = 1

ϕR​ = θ

\(\rm \cos\phi_R=\cos \theta=\frac{R}{\sqrt{R^2+X^2}}\)

% Voltage Regulation vs Power Factor

Now we can conclude various things in relation to the voltage regulation and the power factor which are mentioned below one by one:

1. Zero voltage regulation is possible only for leading power factor load.

2. Maximum voltage regulation is possible only when the load is of lagging or inductive nature.

3. For leading loads, voltage regulation can be zero, positive or negative.

4. For lagging loads, voltage regulation is always positive.

The correct answer is option 1.

Voltage regulation

“Voltage regulation is defined as the ratio of the difference between sending and receiving end voltage to receiving end voltage of a transmission line between the conditions of no load and full load”.

\(VR={V_{R(no \space load)}-V_{R(full\space load)}\over V_R}\)

The receiving end voltage at no-load condition is given by:

\(V_S=AV_R+BI_R\)

At no-load, I_R = 0

\(V_S=AV_R+BI(0)\)

\(V_{R(no\space load)}={V_S\over A}\)

and \(V_{R(full\space load)}=V_R\)

The expression for the voltage regulation in the transmission line is:

\(VR={{V_{S}\over A}-V_{R}\over V_R}\)

• Voltage regulation is a measure of the change in voltage magnitude between the sending and receiving end of the component.
• It is commonly used in power engineering to describe the percentage voltage difference between no-load and full-load voltages distribution lines, transmission lines, and transformers.
• Voltage drop occurs when the voltage at the end of a run of calls is lower than at the beginning.
• Any length or size of wires will have the same resistance and running a current through this dc resistance will cause the voltage to drop.
• As the length of the cable increases, so does its resistance and reactance increase in proportion.
• Hence, the voltage drop is particularly problematic with long cable runs, for example in larger buildings or on more significant properties such as forms.
• Electrical cables carrying current always present inherent resistance, or impedance, to the flow of current.
• Voltage drop is measured as the amount of voltage loss that occurs through all or part of a circuit due to cable ‘impedance’ in volts.
• A larger voltage drop in a cable cross-sectional area can cause lights to flicker or XYZ lively, heaters to heat poorly, and motors to run hotter than normal and turn out.
• This condition causes the load to work harder with less voltage pushing the current.
• To improve voltage regulation (or to decrease voltage drop) in a circuit, one needs to increase the cross-sectional size of the conductors. This is done to lower the overall resistance of the cable length.

Note:

Larger copper or aluminum cable sizes increases cost, so its important to calculate voltage drop and find the optimum voltage wire size that will reduce voltage drop to safe levels while remaining cost-effective.

Concept of Voltage Regulation and Power Factor:

Voltage regulation (VR) is defined as the difference between the sending end voltage (V_S) and the receiving end voltage (V_R), expressed as a fraction of the receiving end voltage:

VR = (V_S - V_R) / V_R

For a leading power factor load, the voltage regulation can be affected by the inductive reactance (X_L) and the line resistance (R) of the transmission line. The expression for voltage regulation in terms of these parameters is:

VR = (I R cosϕ_R) - (I X_L sinϕ_R)

Where,

• I = Line Current
• R = Line Resistance
• X_L = Line Reactance
• V_R = Receiving End Voltage
• cosϕ_R = Load Power Factor (leading)
   

Given Condition:

• The receiving end voltage (V_R) is more than the sending end voltage (V_S), indicating a leading load power factor. This condition implies that the reactive component is capacitive, causing the voltage to rise.
• In a transmission line with a leading power factor, the voltage regulation is negative, meaning the receiving end voltage (VR) is higher than the sending end voltage. The leading power factor causes the capacitive reactance to dominate, which means the reactive component (IXL) plays a larger role than the resistive component (IR). This leads to the condition where IR COSϕR is less than IXLCOSϕR.
   

Correct Expression for Leading Power Factor: IR cosϕ_R < I X_L cosϕ_R

Conclusion:

Hence, the correct expression for the leading load power factor is:

IR cosϕ_R < I X_L cosϕ_R