Power Flow in HVDC Transmission MCQ Quiz - Objective Question with Answer for Power Flow in HVDC Transmission - Download Free PDF

Explanation:

Phase Shift Transformer Power Rating Calculation

Definition: A phase shift transformer is a specialized electrical transformer designed to control the power flow in transmission lines by altering the phase angle of the voltage. This allows it to manage the direction and magnitude of power flow in the network.

Problem Statement: The phase shift transformer is used to control 150 MVA on a 230 kV, 3-phase line, with the phase angle variable between 0 and ±15 degrees. We aim to calculate the approximate basic power rating of the transformer.

Step-by-Step Solution:

The power flow in a transmission line is given by the formula:

P = V₁V₂/X × sin(δ)

Where:

• P = Active Power (MW or MVA)
• V₁ and V₂ = Line-to-line voltages at the two ends of the transmission line (in kV)
• X = Reactance of the transmission line (in ohms)
• δ = Phase angle difference between the voltages (in radians)

For a phase shift transformer, the power flow change it controls is directly related to the phase angle it introduces. The power controlled by the transformer, P_control, is given by:

P_control = (V²/X) × sin(δ)

Here, we assume that the transformer controls a maximum power flow of 150 MVA when the phase angle δ = ±15 degrees.

Step 1: Express the formula for the power controlled.

Let the reactance of the transformer be X_T. The power controlled by the transformer is:

P_control = (V²/X_T) × sin(δ)

Substituting the given values:

• P_control = 150 MVA
• V = 230 kV (line-to-line voltage)
• δ = ±15 degrees = ±15 × (π/180) radians = ±0.2618 radians

Step 2: Rearrange the formula to find X_T.

The reactance of the transformer, X_T, can be calculated as:

X_T = (V² × sin(δ)) / P_control

Substitute the known values:

• V = 230 kV = 230 × 10³ V
• sin(δ) = sin(15 degrees) ≈ 0.2588
• P_control = 150 × 10⁶ W (since 1 MVA = 10⁶ W)

Thus:

X_T = ((230 × 10³)² × 0.2588) / (150 × 10⁶)

Perform the calculations step-by-step:

• (230 × 10³)² = 230² × 10⁶ = 52900 × 10⁶
• (52900 × 10⁶) × 0.2588 = 1367792 × 10⁶
• X_T = (1367792 × 10⁶) / (150 × 10⁶) ≈ 9.12 Ω

Step 3: Calculate the basic power rating of the transformer.

The basic power rating of the transformer corresponds to the voltage and current it handles. Using the apparent power formula:

S = V × I

The current through the transformer is given by:

I = V / X_T

Substitute the values:

• V = 230 × 10³ V
• X_T ≈ 9.12 Ω

I = (230 × 10³) / 9.12 ≈ 25222 A

Now, calculate the apparent power:

S = V × I = (230 × 10³) × (25222) ≈ 150 × 10⁶ VA = 150 MVA

Conclusion: The basic power rating of the phase shift transformer is approximately 150 MVA.

Important Information:

To further understand the analysis, let’s evaluate the other options:

Option 2: 56 MVA

This value is significantly lower than the actual power rating of the transformer. A phase shift transformer controlling 150 MVA power flow cannot have a basic power rating as low as 56 MVA. The basic power rating must at least match the controlled power flow.

Option 3: 75 MVA

This value is also too low to represent the actual basic power rating of the transformer. While it is closer to the correct value than 56 MVA, it still underestimates the required rating for a transformer controlling 150 MVA on a 230 kV line.

Option 4: 750 MVA

This value is excessively high and unrealistic for the given parameters. A transformer with a 750 MVA rating would be designed for much larger systems and power flows than specified in the problem.

Conclusion: The correct option is Option 1: 150 MVA, as it accurately represents the basic power rating of the phase shift transformer required to control 150 MVA power flow on a 230 kV line.

Types of HVDC Link

Monopolar Link:

It has a single conductor of negative polarity and uses earth or sea for the return path of current. Sometimes the metallic return is also used. In the Monopolar link, two converters are placed at the end of each pole.

Bipolar Link:

• The Bipolar link has two conductors one is positive, and the other one is negative to the earth.
• The link has a converter station at each end. The midpoints of the converter stations are earthed through electrodes.
• The voltage of the earthed electrodes is just half the voltage of the conductor used for transmission of the HVDC.
• It has two independent circuits and can be operated as a monopolar link in an emergency.

Homopolar Link:

It has two conductors of the same polarity usually negative polarity, and always operates with earth or metallic return. In the homopolar link, poles are operated in parallel, which reduces the insulation cost.

In the homopolar link, poles are operated in parallel, which reduces the insulation cost.

Explanation:

Monopolar link: It has a single conductor of negative polarity and uses earth or sea for the return path of current. Sometimes the metallic return is also used. In the Monopolar link, two converters are placed at the end of each pole.

Bipolar link:

• The Bipolar link has two conductors one is positive, and the other one is negative to the earth.
• The link has a converter station at each end. The midpoints of the converter stations are earthed through electrodes.
• The voltage of the earthed electrodes is just half the voltage of the conductor used for transmission of the HVDC.
• It has two independent circuits and can be operated as a monopolar link in an emergency.

Homopolar link: It has two conductors of the same polarity usually negative polarity, and always operates with earth or metallic return. In the homopolar link, poles are operated in parallel, which reduces the insulation cost.

• In a Variable Voltage Variable Frequency (VVVF) drive system, the DC link plays a crucial role in providing a clean, stable DC voltage that is fed to the inverter section for conversion into AC at variable frequency and voltage.

​Functions of DC Link:

• Rectification Process: The input AC supply is first converted into DC by a rectifier circuit.
  However, the DC output from the rectifier may contain ripple components or noise, which can affect the performance of the inverter and drive.

• Filtering DC Output: The DC link consists of capacitors or inductors that filter out the ripple and ensure a pure, smooth DC supply.
  This helps maintain stable DC voltage for the inverter, ensuring efficient performance of the drive system.

• Energy Storage: In addition to filtering, the DC link also stores energy, which can be useful during transient conditions or voltage sags.

HVDC Transmission:

• High voltage direct current (HVDC) power systems use D.C. for transmission of bulk power over long distances.
• This type of transmission is preferred over HVAC transmission for very long distances when considering the cost, losses, and many other factors.
• In an HVDC transmission system, generated AC voltage is converted into DC at the sending end. Then, the DC voltage is inverted to AC at the receiving end, for distribution purposes.
• This conversion is performed by a two-six pulse converters units.
• This converter consists of two six pulse converters connected in series on the DC side to meet the voltage requirements.
• Thus, there will be a rectifier terminal at one end of the HVDC substation and an inverter terminal at the other end. 
• Each unit consists of smoothing reactors which are current limiting inductors.
•  It is used to avoid commutation failures occurring in inverters, reduces harmonics, and avoids discontinuation of current for loads.

HVDC transmission system:

The massive transmission of electricity in the form of DC over long distances by means of submarine cables or overhead transmission lines is the high voltage direct current (HVDC) transmission.

The AC power is generated in the generating station. This should first be converted into DC. The conversion is done with the help of a rectifier. 

The DC power will flow through the overhead lines. At the user end, this DC has to be converted into AC. For that purpose, an inverter is placed at the receiving end.

Advantages of HVDC transmission:

• Minimum line power losses
• No skin effect
• Good voltage regulation
• Less corona loss and radio interference
• Reactive power compensation is not required

Concept:
Fig (i) shows 100 volts system whereas Fig (ii) shows 200 volts system. Let P be the power delivered and W be power loss in both cases. Let vl and al be the volume and area of x-section for 200 V system and v₂ and a₂ for that of 200 V system.
 

Now, P = V₂I₂ = 100 I₂

And, P = V2I2 = 200 I₂

As same power is delivered in both cases,

100 I₂ = 200 I₂ or l₂ = (100/200)I₁ = 0.5 I₁

power loss in 100 V system W₁ = \(\rm 2I_1^2R_1\)

Power loss in 100 V system W₂ = \(\rm 2I_2^2R_2\) = 2(0.5I₁)²R₂ = \(\rm 0.5I_1^2R_2\)

As power loss in the two cases in the same,

W₁ = W₂

or

R₂/R₁ = 2/0.5 = 4

or 

\(\rm \frac{a_1}{a_2}=4\)

\(\rm \frac{V_1}{V_2}=4\)

V₂/V₁ = 1/4 = 0.25

%age saving in feeder copper = \(\rm \frac{V_1-V_2}{V_1}× 100=\left(\frac{V_1}{V_1}-\frac{V_2}{V_1}\right)×100\)

= (1 - 0.25) × 100 = 75%

HVDC Transmission:

• High voltage direct current (HVDC) power systems use D.C. to transmit bulk power over long distances.
• In an HVDC transmission system, generated AC voltage is converted into DC at the sending end. Then, the DC voltage is inverted to AC at the receiving end, for distribution purposes.
• A two-six pulse converters units perform this conversion.
• The two-six pulse converters are connected in series on the DC side.
• The two-six pulse converters are connected in parallel on the AC side.
• The two six-pulse converters are fed from delta-delta and delta-star transformers.
• The two secondaries cause displacement of 180°.
• If one unit is working at 60°(rectification mode), then will operate at 120°(inversion mode).

Monopolar link: It has a single conductor of negative polarity and uses earth or sea for the return path of current. Sometimes the metallic return is also used. In the Monopolar link, two converters are placed at the end of each pole.

Bipolar link:

• The Bipolar link has two conductors one is positive, and the other one is negative to the earth.
• The link has a converter station at each end. The midpoints of the converter stations are earthed through electrodes.
• The voltage of the earthed electrodes is just half the voltage of the conductor used for transmission of the HVDC.
• It has two independent circuits and can be operated as a monopolar link in an emergency.

Homopolar link: It has two conductors of the same polarity usually negative polarity, and always operates with earth or metallic return. In the homopolar link, poles are operated in parallel, which reduces the insulation cost.

Skin effect is absent in the HVDC system. Due to dc supply, the current distribution is the same on the wire so there is no skin effect.

Advantages of HVDC transmission:

• No Skin Effect: In HVDC transmission current distributes uniformly over the cross-section of the conductor. Hence no loss due to skin effect is encountered. For the same current-carrying capacity HVDC lines have lesser cross-section compared to HVAC lines
• HVDC transmission operates at unity power factor due to dc supply generally inductive and capacitive elements are absent.
• Lower Transmission Losses: HVDC transmission requires only two conductors. Therefore the power loss in the DC line will be lesser compared to the AC line
• Good voltage Regulation: In DC lines, a voltage drop does not exist due to inductive reactance. Voltage Regulation will be better in HVDC transmission
• Surge Impedance Loading: Long EHV lines are loaded to less than 80% of the natural load. No such condition is applicable in HVDC transmission
• No Line Loading Limit: The permissible loading limit on EHV AC lines is limited by the transient stability limit and the line reactance to almost one-third of the thermal rating of the conductors. No such limitations exist in the case of HVDC line
• Lesser Corona Loss and Radio Interference: Corona Loss directly proportional to frequency. Therefore in the DC line, corona loss will be lesser compared to the AC line.
• Higher Operating Voltages: The design of Insulation of the conductors for high voltage transmission lines depends on the switching surges but not on lightning surges (for voltages beyond 400kV switching surges are more severe than lightning surges). The level of switching surge will be lesser in the DC line compared to the AC line. Hence less insulation is required in DC line
• Reactive Power Compensation: Unlike the AC line DC line does not require any reactive power compensation devices. This is because of the absence of charging currents and power factor operation.
• Short circuit currents during a fault in DC line will be lesser compared to AC lines.
• Absence of the charging currents and limitations on the cable lengths.
• Economical and greater reliability.

Disadvantages of HVDC transmission:

• Converter substations are required at both the sending and the receiving end of the transmission lines, which result in increasing the cost.
• Inverter and rectifier terminals generate harmonics which is reduced using active filters which are also very expensive.
• The inverter used in Converter substations has limited overload capacity.
• Circuit breakers are used in HVDC for circuit breaking, which is also very expensive.
• It does not have transformers for changing the voltage levels.

High voltage direct current transmission of bulk power over long distances.

Advantages of HVDC transmission:

• No Skin Effect: In HVDC transmission current distributes uniformly over the cross-section of the conductor. Hence no loss due to skin effect is encountered. For the same current-carrying capacity HVDC lines have lesser cross-section compared to HVAC lines
• Lower Transmission Losses: HVDC transmission requires only two conductors. Therefore the power loss in the DC line will be lesser compared to the AC line
• Good voltage Regulation: In DC lines, a voltage drop does not exist due to inductive reactance. Voltage Regulation will be better in HVDC transmission
• Surge Impedance Loading: Long EHV lines are loaded to less than 80% of the natural load. No such condition is applicable in HVDC transmission
• No Line Loading Limit: The permissible loading limit on EHV AC lines is limited by the transient stability limit and the line reactance to almost one-third of the thermal rating of the conductors. No such limitations exist in the case of HVDC line
• Lesser Corona Loss and Radio Interference: Corona Loss directly proportional to frequency. Therefore in the DC line, corona loss will be lesser compared to the AC line.
• Higher Operating Voltages: The design of Insulation of the conductors for high voltage transmission lines depends on the switching surges but not on lightning surges (for voltages beyond 400kV switching surges are more severe than lightning surges). The level of switching surge will be lesser in the DC line compared to the AC line. Hence less insulation is required in DC line
• Reactive Power Compensation: Unlike the AC line DC line does not require any reactive power compensation devices. This is because of the absence of charging currents and power factor operation.
• Short circuit currents during a fault in DC line will be lesser compared to AC lines.
• Absence of the charging currents and limitations on the cable lengths.
• Economical and greater reliability.

HVDC Transmission:

• High voltage direct current (HVDC) power systems use D.C. for transmission of bulk power over long distances.
• This type of transmission is preferred over HVAC transmission for very long distances when considering the cost, losses, and many other factors.
• In an HVDC transmission system, generated AC voltage is converted into DC at the sending end. Then, the DC voltage is inverted to AC at the receiving end, for distribution purposes.
• This conversion is performed by a two-six pulse converters units.
• This converter consists of two six pulse converters connected in series on the DC side to meet the voltage requirements.
• Thus, there will be a rectifier terminal at one end of the HVDC substation and an inverter terminal at the other end. 
• Each unit consists of smoothing reactors which are current limiting inductors.
•  It is used to avoid commutation failures occurring in inverters, reduces harmonics, and avoids discontinuation of current for loads.

Monopolar link: It has a single conductor of negative polarity and uses earth or sea for the return path of current. Sometimes the metallic return is also used. In the Monopolar link, two converters are placed at the end of each pole.

Bipolar link:

• The Bipolar link has two conductors one is positive, and the other one is negative to the earth.
• The link has a converter station at each end. The midpoints of the converter stations are earthed through electrodes.
• The voltage of the earthed electrodes is just half the voltage of the conductor used for transmission of the HVDC.
• It has two independent circuits and can be operated as a monopolar link in an emergency.

Homopolar link: It has two conductors of the same polarity usually negative polarity, and always operates with earth or metallic return. In the homopolar link, poles are operated in parallel, which reduces the insulation cost.

Explanation:

Phase Shift Transformer Power Rating Calculation

Definition: A phase shift transformer is a specialized electrical transformer designed to control the power flow in transmission lines by altering the phase angle of the voltage. This allows it to manage the direction and magnitude of power flow in the network.

Problem Statement: The phase shift transformer is used to control 150 MVA on a 230 kV, 3-phase line, with the phase angle variable between 0 and ±15 degrees. We aim to calculate the approximate basic power rating of the transformer.

Step-by-Step Solution:

The power flow in a transmission line is given by the formula:

P = V₁V₂/X × sin(δ)

Where:

• P = Active Power (MW or MVA)
• V₁ and V₂ = Line-to-line voltages at the two ends of the transmission line (in kV)
• X = Reactance of the transmission line (in ohms)
• δ = Phase angle difference between the voltages (in radians)

For a phase shift transformer, the power flow change it controls is directly related to the phase angle it introduces. The power controlled by the transformer, P_control, is given by:

P_control = (V²/X) × sin(δ)

Here, we assume that the transformer controls a maximum power flow of 150 MVA when the phase angle δ = ±15 degrees.

Step 1: Express the formula for the power controlled.

Let the reactance of the transformer be X_T. The power controlled by the transformer is:

P_control = (V²/X_T) × sin(δ)

Substituting the given values:

• P_control = 150 MVA
• V = 230 kV (line-to-line voltage)
• δ = ±15 degrees = ±15 × (π/180) radians = ±0.2618 radians

Step 2: Rearrange the formula to find X_T.

The reactance of the transformer, X_T, can be calculated as:

X_T = (V² × sin(δ)) / P_control

Substitute the known values:

• V = 230 kV = 230 × 10³ V
• sin(δ) = sin(15 degrees) ≈ 0.2588
• P_control = 150 × 10⁶ W (since 1 MVA = 10⁶ W)

Thus:

X_T = ((230 × 10³)² × 0.2588) / (150 × 10⁶)

Perform the calculations step-by-step:

• (230 × 10³)² = 230² × 10⁶ = 52900 × 10⁶
• (52900 × 10⁶) × 0.2588 = 1367792 × 10⁶
• X_T = (1367792 × 10⁶) / (150 × 10⁶) ≈ 9.12 Ω

Step 3: Calculate the basic power rating of the transformer.

The basic power rating of the transformer corresponds to the voltage and current it handles. Using the apparent power formula:

S = V × I

The current through the transformer is given by:

I = V / X_T

Substitute the values:

• V = 230 × 10³ V
• X_T ≈ 9.12 Ω

I = (230 × 10³) / 9.12 ≈ 25222 A

Now, calculate the apparent power:

S = V × I = (230 × 10³) × (25222) ≈ 150 × 10⁶ VA = 150 MVA

Conclusion: The basic power rating of the phase shift transformer is approximately 150 MVA.

Important Information:

To further understand the analysis, let’s evaluate the other options:

Option 2: 56 MVA

This value is significantly lower than the actual power rating of the transformer. A phase shift transformer controlling 150 MVA power flow cannot have a basic power rating as low as 56 MVA. The basic power rating must at least match the controlled power flow.

Option 3: 75 MVA

This value is also too low to represent the actual basic power rating of the transformer. While it is closer to the correct value than 56 MVA, it still underestimates the required rating for a transformer controlling 150 MVA on a 230 kV line.

Option 4: 750 MVA

This value is excessively high and unrealistic for the given parameters. A transformer with a 750 MVA rating would be designed for much larger systems and power flows than specified in the problem.

Conclusion: The correct option is Option 1: 150 MVA, as it accurately represents the basic power rating of the phase shift transformer required to control 150 MVA power flow on a 230 kV line.

Types of HVDC Link

Monopolar Link:

It has a single conductor of negative polarity and uses earth or sea for the return path of current. Sometimes the metallic return is also used. In the Monopolar link, two converters are placed at the end of each pole.

Bipolar Link:

• The Bipolar link has two conductors one is positive, and the other one is negative to the earth.
• The link has a converter station at each end. The midpoints of the converter stations are earthed through electrodes.
• The voltage of the earthed electrodes is just half the voltage of the conductor used for transmission of the HVDC.
• It has two independent circuits and can be operated as a monopolar link in an emergency.

Homopolar Link:

It has two conductors of the same polarity usually negative polarity, and always operates with earth or metallic return. In the homopolar link, poles are operated in parallel, which reduces the insulation cost.