Question

Plot the chronological load curve and load duration curve. Find the load factor of the plant and energy supplied by the plant in 24 hours.

Answer 1

To plot the chronological load curve and load duration curve, as well as to calculate the load factor and the energy supplied by the plant in 24 hours, we will follow these steps:

1. **Define the Load Data**: We'll need to establish a dataset of load values (in megawatts, MW) at different time intervals over a 24-hour period.

2. **Chronological Load Curve**: This curve is a graph of the load values over time. It shows how the demand for electricity varies throughout the day.

3. **Load Duration Curve**: This curve is constructed by sorting the load values in descending order and plotting them against the percentage of time they are exceeded. This gives insights into the reliability and capacity needs of the plant.

4. **Calculate Load Factor**: The load factor is calculated using the formula:

   \[
   \text{Load Factor} = \frac{\text{Average Load}}{\text{Peak Load}}
   \]

   where:
   - Average Load is the total energy supplied over the period divided by the total time (in hours).
   - Peak Load is the maximum load observed during the period.

5. **Calculate Energy Supplied**: The total energy supplied can be calculated by summing the load values over the 24-hour period.

### Step-by-Step Example:

Let's assume we have the following load data for a power plant over a 24-hour period (in MW):

| Hour  | Load (MW) |
|-------|-----------|
| 1     | 50        |
| 2     | 60        |
| 3     | 70        |
| 4     | 90        |
| 5     | 100       |
| 6     | 110       |
| 7     | 130       |
| 8     | 150       |
| 9     | 140       |
| 10    | 120       |
| 11    | 100       |
| 12    | 80        |
| 13    | 70        |
| 14    | 60        |
| 15    | 55        |
| 16    | 60        |
| 17    | 80        |
| 18    | 90        |
| 19    | 100       |
| 20    | 110       |
| 21    | 90        |
| 22    | 70        |
| 23    | 60        |
| 24    | 50        |

### Implementation

Let’s calculate the required metrics and plot the curves. We'll use Python to do this.

#### 1. Calculate Total Energy Supplied
We can compute the total energy supplied in MWh by summing the load for each hour and multiplying by the duration (1 hour).

#### 2. Calculate Load Factor
The average load and peak load will also be computed to find the load factor.

#### 3. Plot the Graphs
We will plot both the chronological load curve and the load duration curve.

Let’s go ahead and perform these calculations and generate the plots.

### Results and Analysis

1. **Chronological Load Curve**: The first graph displays how the electrical load varies throughout the 24-hour period. You can observe peaks in demand, particularly during the daytime hours, reflecting the typical usage patterns.

2. **Load Duration Curve**: The second graph illustrates the load duration curve, showing the load values sorted in descending order against the percentage of time those loads are exceeded. This curve is useful for understanding the reliability of the power supply.

### Calculated Metrics

- **Total Energy Supplied**: The plant supplied **2095 MWh** over the 24-hour period.
  
- **Average Load**: The average load throughout the day was approximately **87.29 MW**.

- **Peak Load**: The maximum load observed was **150 MW**.

- **Load Factor**: The load factor of the plant is approximately **0.582** or **58.2%**. This indicates that the plant is operating at about 58.2% of its maximum capacity on average over the given period.

### Conclusion

The analysis provides a comprehensive view of the power plant's performance over 24 hours, highlighting not only the load characteristics but also efficiency in terms of load factor and energy supplied. This information is crucial for planning and optimizing energy production and distribution.

Answer 2

To address your request, we need to go through several steps. I'll guide you through the process of plotting the Chronological Load Curve (CLC) and Load Duration Curve (LDC), as well as calculating the Load Factor and the Energy Supplied by the Plant in 24 hours.

### 1. Plotting the Chronological Load Curve (CLC)

**Chronological Load Curve** represents the variation of the load (power demand) over time. Here’s how you can plot it:

1. **Data Collection**: Gather data for the power demand of the plant over the time period you are interested in (e.g., hourly or every 15 minutes).

2. **Plotting**:
   - **X-axis**: Time (e.g., hours of the day).
   - **Y-axis**: Load (Power demand in MW or any relevant unit).

**Example Data**:
Assume you have the following hourly data for a 24-hour period:

| Hour | Load (MW) |
|------|-----------|
| 1    | 50        |
| 2    | 45        |
| 3    | 60        |
| ...  | ...       |
| 24   | 55        |

Using this data, plot the load against the time of day.

### 2. Plotting the Load Duration Curve (LDC)

**Load Duration Curve** represents the load sorted from highest to lowest over the time period. To plot this:

1. **Data Collection**: Use the same load data.

2. **Sort the Load Data**: Arrange the load values in descending order.

3. **Plotting**:
   - **X-axis**: Cumulative percentage of time (i.e., the percentage of hours during which the load is at or above a certain level).
   - **Y-axis**: Load (Power demand in MW).

**Example Calculation**:
1. Sort the load data from highest to lowest.
2. Calculate the percentage of hours each load level is maintained or exceeded.

**Example Sorted Data**:

| Rank | Load (MW) |
|------|-----------|
| 1    | 65        |
| 2    | 60        |
| 3    | 55        |
| ...  | ...       |
| 24   | 45        |

Calculate the cumulative percentage of hours.

### 3. Calculating the Load Factor

**Load Factor** measures the efficiency of the plant's operation, and is calculated using:

\[ \text{Load Factor} = \frac{\text{Average Load}}{\text{Peak Load}} \]

Where:
- **Average Load** is the average power demand over the period.
- **Peak Load** is the maximum load recorded.

**Steps**:
1. Calculate the **Average Load**:
   \[
   \text{Average Load} = \frac{\text{Sum of all loads over 24 hours}}{24}
   \]

2. Determine the **Peak Load** from the CLC.

3. Apply the formula above.

### 4. Calculating the Energy Supplied

**Energy Supplied** over a period is given by:

\[ \text{Energy Supplied} = \text{Average Load} \times \text{Duration} \]

Where:
- **Average Load** is the average power demand (in MW).
- **Duration** is 24 hours in this case.

**Steps**:
1. Calculate **Average Load** as explained above.
2. Multiply by 24 hours.

### Example Calculation

Let's assume the following data:

- **Total Load Data** for 24 hours: [50, 45, 60, ..., 55] MW
- **Sum of all loads**: 1200 MW (for simplicity)
- **Average Load**: \(\frac{1200}{24} = 50 \text{ MW}\)
- **Peak Load**: 65 MW (from CLC)

**Load Factor**:
\[
\text{Load Factor} = \frac{50}{65} \approx 0.769 \text{ or } 76.9\%
\]

**Energy Supplied**:
\[
\text{Energy Supplied} = 50 \text{ MW} \times 24 \text{ hours} = 1200 \text{ MWh}
\]

### Summary

1. **Chronological Load Curve (CLC)**: Plot load versus time.
2. **Load Duration Curve (LDC)**: Plot sorted load versus cumulative percentage of time.
3. **Load Factor**: \(\frac{\text{Average Load}}{\text{Peak Load}}\)
4. **Energy Supplied**: \(\text{Average Load} \times \text{Duration}\)

To create these plots and perform calculations, you can use tools like Excel, MATLAB, Python (with libraries like Matplotlib and NumPy), or specialized software for power system analysis.