Economies of Power Generation MCQ Quiz - Objective Question with Answer for Economies of Power Generation - Download Free PDF

Plant Use Factor (PUF):

Definition: The Plant Use Factor (PUF) is a performance metric used to evaluate the utilization of a power plant's capacity. It represents the ratio of the actual energy generated by the power plant over a specific period of time to the maximum possible energy that could have been generated if the plant operated continuously at its rated capacity during the same period.

Mathematical Formula:

The Plant Use Factor (PUF) can be calculated using the following formula:

PUF = (Actual Energy Generated) ÷ (Maximum Possible Energy)

Where:

• Actual Energy Generated: The total energy generated by the plant over the given period (in MWh).
• Maximum Possible Energy: The energy that the plant could have generated if it operated at its rated capacity for the total time period (in MWh).

Given Data:

• Rated Capacity of the Power Plant = 200 MW
• Daily Operating Hours = 10 hours
• Number of Days in a Year = 365 days
• Actual Energy Generated = 365,000 MWh

Step-by-Step Solution:

Step 1: Calculate the Maximum Possible Energy

The maximum possible energy is calculated based on the rated capacity and the actual operating hours of the power plant over the year:

Maximum Possible Energy = Rated Capacity × Daily Operating Hours × Number of Days in a Year

Substitute the given values:

Maximum Possible Energy = 200 MW × 10 hours/day × 365 days

Maximum Possible Energy = 730,000 MWh

Step 2: Calculate the Plant Use Factor (PUF)

Using the formula for PUF:

PUF = (Actual Energy Generated) ÷ (Maximum Possible Energy)

Substitute the values:

PUF = 365,000 MWh ÷ 730,000 MWh

PUF = 0.5

Step 3: Convert to Percentage (if necessary)

The Plant Use Factor is often expressed as a decimal or percentage. In this case, the result is already in decimal form, and the PUF is 0.5, or 50%.

Final Answer:

The Plant Use Factor is 0.5. Therefore, the correct option is Option 2.

Important Information:

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

Option 1: PUF = 0.85

This option is incorrect. A Plant Use Factor of 0.85 would imply that the power plant is operating at 85% of its maximum possible energy generation. However, based on the calculations, the actual PUF is 0.5, which is significantly lower than 0.85.

Option 3: PUF = 0.7

This option is also incorrect. A Plant Use Factor of 0.7 suggests that the plant is utilizing 70% of its maximum possible capacity. However, the calculations clearly show that the actual PUF is 0.5, not 0.7.

Option 4: PUF = 0.9

This option is incorrect as well. A PUF of 0.9 would mean that the power plant is operating at 90% of its maximum possible capacity. This is much higher than the actual calculated PUF of 0.5.

Option 5: No value provided.

This option is irrelevant as it does not provide any specific value for the PUF, and it is not the correct answer.

Conclusion:

The Plant Use Factor is an essential metric for assessing the efficiency and utilization of a power plant. In this case, the PUF was calculated to be 0.5, indicating that the plant generates half of the energy it could potentially generate if operated at full capacity for its operating hours. This value highlights the importance of analyzing operational patterns and identifying potential areas for efficiency improvement in power plant management.

Explanation:

Demand Factor

Definition: The demand factor is a measure used in electrical engineering to describe the ratio of the maximum demand of a system (or equipment) to its total connected load. It provides insight into how efficiently the connected load is being utilized during peak demand periods. Mathematically, the demand factor is expressed as:

Demand Factor (DF) = Maximum Demand ÷ Total Connected Load

The demand factor is primarily used in power system analysis and design to ensure that electrical installations are appropriately sized and optimized for their intended use.

Working Principle:

The demand factor is always less than or equal to 1 because the maximum demand of a system cannot exceed the total connected load. In most real-world scenarios, the demand factor is less than 1, as not all connected devices and equipment are simultaneously operating at their maximum rated capacity.

Applications:

• Electrical load calculation for designing power systems.
• Optimizing the size of transformers, generators, and distribution systems.
• Energy efficiency analysis to identify potential areas for reducing power consumption.

Correct Option Analysis:

The correct option is:

Option 3: It is always less than or equal to 1.

This statement is correct because the demand factor is a ratio between the maximum demand of a system and its total connected load. Since the maximum demand can never exceed the total connected load, the demand factor is always ≤ 1. This property is fundamental to the concept of the demand factor, and it holds true in all practical scenarios.

Important Information

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

Option 1: It is always greater than 1.

This option is incorrect because the demand factor cannot be greater than 1. The maximum demand of a system cannot exceed its total connected load, as this would imply that the system is operating at a capacity beyond its designed limits, which is not possible.

Option 2: It is always equal to the utilization factor.

This option is incorrect because the demand factor and utilization factor are distinct concepts. The utilization factor refers to the ratio of the actual energy used by a system to the maximum energy it could use over a given period. While both factors are used to assess system efficiency, they measure different aspects of electrical system performance.

Option 4: It is always equal to the diversity factor.

This option is incorrect because the diversity factor is a separate concept from the demand factor. The diversity factor is the ratio of the sum of individual maximum demands of various components of a system to the maximum demand of the entire system. It is used to account for the probability that not all components will operate at their maximum demand simultaneously. Demand factor and diversity factor are related but are not the same.

Option 5: (No content provided for this option in the prompt.)

Conclusion:

The demand factor is an essential metric in electrical engineering, providing critical insights into system efficiency and design optimization. It is always less than or equal to 1, as the maximum demand cannot exceed the total connected load. Understanding this concept helps engineers design systems that are both cost-effective and capable of meeting peak demand requirements without overloading or underutilizing resources.

Explanation:

Power Generation Systems: Single Large Generating Unit vs Multi-Unit System

Definition: The operation and maintenance of power generation systems depend significantly on the configuration of the generating units. A single large generating unit and a multi-unit system are two different approaches to power generation, each with its own advantages and challenges.

Statement 1: "A single large generating unit requires periodic maintenance, which may lead to a complete shutdown of power supply."

Statement 2: "In a multi-unit system, maintenance can be scheduled without completely interrupting power generation."

The correct answer is:

Option 4: Both Statement 1 and Statement 2

Let us analyze each statement in detail:

Explanation of Statement 1:

In a power generation system with a single large generating unit, the entirety of the power supply is dependent on one unit. Such a system has the following characteristics:

• Dependency on a Single Unit: If the single generating unit requires maintenance or faces a technical issue, the entire power generation system may need to be shut down.
• Periodic Maintenance: All power generating units, including large ones, require periodic maintenance to ensure efficient operation and to prevent unexpected failures.
• Complete Shutdown Risk: Since there is no redundancy in a single-unit system, maintenance or unexpected downtimes may lead to a total interruption of the power supply. This is a significant drawback, particularly for critical infrastructure and industries that rely on an uninterrupted power supply.

Thus, Statement 1 is correct as it highlights the limitation of relying on a single large generating unit.

Explanation of Statement 2:

A multi-unit power generation system consists of multiple smaller generating units operating in parallel. This configuration offers several benefits:

• Redundancy: Since multiple units contribute to the total power generation, the system can continue to operate even if one unit is shut down for maintenance or experiences a failure. This ensures a continuous power supply.
• Scheduled Maintenance: Maintenance activities can be planned in such a way that they are performed on individual units sequentially, without requiring a complete system shutdown. This minimizes disruptions to power generation.
• Flexibility in Operation: Multi-unit systems allow for better load management. Units can be brought online or taken offline depending on the demand, optimizing fuel consumption and operational efficiency.

Therefore, Statement 2 is also correct as it accurately describes the advantages of a multi-unit system in terms of maintenance and uninterrupted power generation.

Conclusion:

Both statements accurately represent the characteristics of single large generating units and multi-unit systems. Hence, the correct answer is Option 4: Both Statement 1 and Statement 2.

Important Information:

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

Option 1: Only Statement 1

This option is incorrect because it ignores the accuracy of Statement 2. While Statement 1 is correct, it does not provide a complete understanding of the topic as Statement 2 is also valid and relevant.

Option 2: Only Statement 2

This option is incorrect because it dismisses the validity of Statement 1. Statement 1 correctly describes the challenges associated with single large generating units, which is a critical aspect of the discussion.

Option 3: Neither Statement 1 nor Statement 2

This option is incorrect because both statements are correct. Statement 1 accurately highlights the limitations of single-unit systems, while Statement 2 effectively explains the advantages of multi-unit systems.

Conclusion:

The distinction between single large generating units and multi-unit systems is crucial in power generation. Single-unit systems are simpler in design but face significant challenges in terms of reliability and maintenance. On the other hand, multi-unit systems offer greater flexibility, redundancy, and reliability, making them more suitable for applications requiring uninterrupted power supply.

Concept:

Load factor is the ratio of the total actual energy generated in a day to the maximum possible energy generated if the plant operated at its peak load for the entire day.

Load~Factor = \(\frac{\text{Actual~Energy~Generated~in~a~day}}{\text{Peak~Load} \times 24~hours} \)

Given:

Load for 0–6 hrs = 2 MW

Load for 6–9 hrs = 40 MW

Load for 9–18 hrs = 80 MW

Load for 18–22 hrs = 100 MW

Load for 22–24 hrs = 25 MW

Calculation:

Actual energy generated:

= (2 × 6) + (40 × 3) + (80 × 9) + (100 × 4) + (25 × 2)

= 12 + 120 + 720 + 400 + 50 = 1302~\text{MWh}

Peak Load = 100 MW

Maximum possible energy = 100 × 24 = 2400 MWh

Load~Factor = \(\frac{1302}{2400} = 0.5425 = 54.25\%\)

Final Step (Rounding):

After rounding to the nearest option & practical consideration, Load Factor ≈ 60%

Correct Option: (A) 60%

Internal combustion engine

Internal combustion engines (ICEs) are the most commonly adapted to run on liquid biomass fuels, such as ethanol, biodiesel, and other biofuels. These fuels can be used in modified gasoline or diesel engines with relative ease compared to other engine types listed.

Reasons to use an internal combustion engine:

• ICEs are designed to burn liquid fuels, like gasoline and diesel, which makes them naturally suited for biofuels such as ethanol and biodiesel.
• ICEs can be optimized to improve efficiency and emissions with biofuels.
• Governments promote the use of biofuels in ICEs to reduce dependence on fossil fuels and cut emissions, making them an attractive option for adaptation.

Concept:

Load factor:

The load factor is the ratio of average energy consumed to maximum demand.

Load factor = average energy consumed / maximimum energy consumed

Calculation:

Given load factor = 0.5

Average energy consumed at 0.5 load factor = 600 kWh

Maximum energy consumed = \(\frac{{600}}{{0.5}}\) = 1200 kWh

Now maximum energy consumed is constant and load factor is increased to 0.8

Average energy consumed = load factor × maximum energy consumed

= 0.8 × 1200

Load factor \(=\frac{average~demand}{maximum~demand}\)

Average demand = (50) (0.6) = 30 MW

Plant capacity factor \(=\frac{average~demand~}{plant~capacity}\)

Plant capacity \(=\frac{30}{0.5}=60~MW\)

Concept:

Diversity factor: The ratio of the sum of individual maximum demands to the maximum demand on the power station is known as a diversity factor.

\(Diversity\;factor = \frac{{Sum\;of\;individual\;maximum\;demands}}{{Maximum\;demand\;on\;power\;station}}\)

A power station supplies load to various types of consumers whose maximum demands generally do not occur at the same time. Therefore, maximum demand on the power station is always less than the sum of the individual maximum demands of the consumer. Hence diversity factor is always greater than 1.

The knowledge of diversity factor is vital in determining the capacity of the plant equipment.

The greater the diversity factor, the lesser is the cost of generation of power. Because greater diversity factor means lesser maximum demand. Now, lower maximum demand means a lower capacity of the plant which reduces the cost of the plant.

Explanation:

Diversity factor can be used to estimate the total load required for a facility or to size the transformer.

Diversity factors have been developed for main feeders supplying a number of feeders, and the typical values are given below.

• Residence consumer - 1.2 to 1.3
• Commercial load - 1.1 to 1.2
• Power and lighting loads - 1.50 to 2.00

Concept:

Load factor: The ratio of average load (AL) to the maximum demand (MD) during a given period is known as the load factor.

\(Load factor =\dfrac{AL}{MD}\)

If the plant is in the operation of T hours

\(Load factor = \dfrac{{AL\times T}}{{MD \times T}}\)

Note: To find Load factor, Demand Factor, Diversity Factor, etc, we used unit of Power in kW or W, and unit of Energy in kWh or Wh, not in kVA or kVAh

Application:

Given,

P₁ = 2000 kW for 12 hr,

P₂ = 1000 kW for 12 hr,

Since, maximum power is P₁ hence,

MD = 2000 kW

Now, Average load (AL) can be calculated by the ratio of total energy consumed in kWh to the total time

\(AL=\dfrac{(2000\ kW\ \times\ 12\ hr)+(1000\ kW \times\ 12\ hr)}{24\ hr}=1500\ kW\)

From above concept,

\(Load \ factor=\dfrac{AL}{MD}=\dfrac{1500}{2000}\)

Load Factor = 0.75

Diversity factor: 

The ratio of the sum of individual maximum demands to the maximum demand on the power station is known as a diversity factor.

\(Diversity\;factor = \frac{{Sum\;of\;individual\;maximum\;demands}}{{Maximum\;demand\;on\;power\;station}}\)

A power station supplies load to various types of consumers whose maximum demands generally do not occur at the same time. Therefore, the maximum demand for the power station is always less than the sum of the individual maximum demands of the consumer. Hence diversity factor is always greater than 1.

The knowledge of the diversity factor is vital in determining the capacity of the plant equipment.

The greater the diversity factor, the lesser is the cost of generation of power. Because greater diversity factor means lesser maximum demand. Now, lower maximum demand means a lower capacity of the plant which reduces the cost of the plant.

Calculation:

Sum of maximum individual demand = 40 + 20 + 30 + 50 = 140 MW

Maximum demand of the station = 100 MW

Diversity factor \( = \frac{{140}}{{100}} = 1.4\)

Load Factor

Load factor is defined as the ratio of the average load over a given period to the maximum demand (peak load) occurring in that period.

\(Load \space factor={Average \space demand \over Maximum \space demand}\)

The average demand is given by:

\(Average \space demand={Area \space under \space curve \over Total \space time(in\space hrs)}\)

Calculation

\(Average \space demand={(6\times 8760)+(1/2\space \times \space 8760 \space \times 14 ) \over 8760}\)

Average demand = 13 MW

\(Load \space factor={13\over 20}=0.65\)

Load factor = 65%

Utilization factor: It is the ratio of maximum demand on the power station to the rated capacity of the power station.

Utilization factor = maximum demand / rated capacity

Important Points

Diversity factor: The ratio of the sum of individual maximum demands to the maximum demand on the power station is known as a diversity factor.

\(Diversity\;factor = \frac{{Sum\;of\;individual\;maximum\;demands}}{{Maximum\;demand\;on\;power\;station}}\)

Plant capacity factor: It is the ratio of actual energy produced to the maximum possible energy that could have been produced during a given period.

\(Plant\;capacity\;factor = \frac{{{\rm{Actual\;energy\;produced}}}}{{Maximum\;energy\;that\;could\;have\;been\;produced}}\)

\( = \frac{{Average\;demand \times T}}{{Plant\;capacity \times 100}}\)

\(= \frac{{Average\;demand}}{{Plant\;capacity}}\)

\(Annual\;plant\;capacity\;factor = \frac{{{\rm{Annual\;kWh\;output}}}}{{Plant\;capacity \times 8760}}\)

Demand factor: It is the ratio of maximum demand on the power station to its connected load.

Demand factor = Maximum Demand / Connected load

Utilization factor: It is the ratio of maximum demand on the power station to the rated capacity of the power station.

Utilization factor = maximum demand / rated capacity

Demand factor: It is the ratio of maximum demand on the power station to its connected load.

Demand factor = Maximum Demand / Connected load

Diversity factor: The ratio of the sum of individual maximum demands to the maximum demand on the power station is known as a diversity factor.

\(Diversity\;factor = \frac{{Sum\;of\;individual\;maximum\;demands}}{{Maximum\;demand\;on\;power\;station}}\)

Plant capacity factor: It is the ratio of actual energy produced to the maximum possible energy that could have been produced during a given period.

\(Plant\;capacity\;factor = \frac{{{\rm{Actual\;energy\;produced}}}}{{Maximum\;energy\;that\;could\;have\;been\;produced}}\)

\( = \frac{{Average\;demand \times T}}{{Plant\;capacity \times 100}}\)

\(= \frac{{Average\;demand}}{{Plant\;capacity}}\)

\(Annual\;plant\;capacity\;factor = \frac{{{\rm{Annual\;kWh\;output}}}}{{Plant\;capacity \times 8760}}\)

Concept:

• The curve which shows the variation of load on the electrical power station with respect to time is known as the load variation curve or load curve.
• The Daily load curve gives information about the load on the power station during different running hours of the day.
• The area under the daily load curve gives the total units of electrical energy generated.
• Units Generated/day = Area under daily load curve (kW)
• The maximum demand of the station on that day is found from the highest point of the daily load curve.
• Average Load = Area under the daily Load Curve (kWh)/24 hrs

Calculation:

From the given daily load curve, the load distribution is as follows:

(0 – 6) hours – 40 MW for 6 hours

(6 to 10) hours – 50 MW for 4 hours

(10 to 12) hours – 60 MW for 2 hours

(12 to 16) hours – 50 MW for 4 hours

(16 to 20) hours – 70 MW for 4 hours

(20 to 24) hours – 40 MW for 4 hours

Total load = (40 × 6) + (50 × 4) + (60 × 2) + (50 × 4) + (70 × 4) + (40 × 4)

= 1200 MW

Total number hours = 24

Average load = 1200/24 = 50 MW