Question

Draw and explain 'V' and 'inverted V curves' for synchronous motor.

Answer 1

The **V-curves** and **inverted V-curves** are graphical representations used to understand the performance of synchronous motors in terms of their reactive power and field current. Here’s a detailed explanation:

### V-Curve for Synchronous Motor

The V-curve shows the relationship between the field current (or excitation current) of a synchronous motor and its reactive power (or power factor) while keeping the motor’s load constant. It is called a V-curve because the plot typically resembles the letter 'V'.

#### **Plot Description:**
- **X-axis:** Field Current (Excitation Current)
- **Y-axis:** Reactive Power (or Power Factor Angle)

#### **Explanation:**
1. **At Low Excitation Currents:**
   - The motor is underexcited. It absorbs reactive power from the supply.
   - The power factor is lagging (inductive behavior), and the reactive power drawn is high.

2. **At Medium Excitation Currents:**
   - The motor is near its synchronous condition, and the reactive power approaches zero.
   - The power factor improves and can become unity (purely resistive).

3. **At High Excitation Currents:**
   - The motor becomes overexcited. It supplies reactive power to the system.
   - The power factor turns leading (capacitive behavior), and the reactive power supplied is high.

### Inverted V-Curve for Synchronous Motor

The inverted V-curve represents the same relationship as the V-curve but with a focus on the power factor angle instead of reactive power.

#### **Plot Description:**
- **X-axis:** Field Current (Excitation Current)
- **Y-axis:** Power Factor Angle (or Power Factor)

#### **Explanation:**
1. **At Low Excitation Currents:**
   - The power factor is lagging, and the angle between the voltage and current is large, indicating significant reactive power absorption.

2. **At Medium Excitation Currents:**
   - The power factor angle decreases, showing that the motor is operating near a unity power factor.

3. **At High Excitation Currents:**
   - The power factor is leading, and the angle between the voltage and current becomes negative, indicating reactive power supply.

### **Key Points:**
- **V-Curve:** Used to determine the reactive power requirement and power factor based on field current.
- **Inverted V-Curve:** Provides insights into how the power factor angle varies with excitation current.

### **Applications:**
These curves are essential for:
- **Stability Analysis:** Ensuring that the motor operates within stable limits.
- **Reactive Power Control:** Adjusting excitation to manage power factor and reactive power in the system.

These graphical tools help engineers and operators in optimizing the performance of synchronous motors in power systems.

Answer 2

### V-Curve and Inverted V-Curve of a Synchronous Motor

#### **1. V-Curve**

**Definition:**
The V-curve of a synchronous motor represents the relationship between the field current (or excitation current) and the power factor (or reactive power) of the motor at a constant load.

**Drawing:**
Imagine a graph with the horizontal axis representing the field current (I_f) and the vertical axis representing the power factor (cos φ) or reactive power (Q).

Here’s what the V-curve typically looks like:

1. **Shape:** It resembles the letter "V" when plotted.
2. **Behavior:**
   - At low field currents, the power factor is lagging (inductive) because the motor is underexcited.
   - As the field current increases, the power factor improves and becomes more leading (capacitive) as the motor reaches the point of excitation where it balances reactive power.
   - Further increasing the field current will bring the power factor back towards lagging if overexcited.

**Explanation:**

- **Underexcited Region:** When the field current is low, the synchronous motor behaves like an inductive load. This causes it to draw lagging reactive power from the supply, leading to a lagging power factor.
- **Critical Point:** At a certain field current, the motor reaches a condition where it supplies or absorbs a balance of reactive power, leading to a power factor of unity or near unity.
- **Overexcited Region:** As the field current continues to increase beyond this critical point, the motor begins to supply leading reactive power, which improves the power factor and makes it more leading.

#### **2. Inverted V-Curve**

**Definition:**
The inverted V-curve represents the relationship between the field current and the reactive power (Q) or power factor of a synchronous motor at a constant load.

**Drawing:**
Imagine a graph with the horizontal axis representing the field current (I_f) and the vertical axis representing the reactive power (Q).

Here’s what the inverted V-curve typically looks like:

1. **Shape:** It resembles an upside-down "V" or an inverted "V" when plotted.
2. **Behavior:**
   - At low field currents, the motor absorbs a large amount of reactive power (inductive behavior).
   - As the field current increases, the reactive power absorbed decreases, and the motor starts to supply reactive power (capacitive behavior).
   - The minimum reactive power (or zero reactive power) is at a particular field current.

**Explanation:**

- **Underexcited Region:** At low field currents, the motor behaves inductively, absorbing reactive power (Q is positive). This is reflected in the upward slope of the curve.
- **Critical Point:** At a specific field current, the motor’s reactive power output reaches a minimum. This point indicates the motor is at or near a power factor of unity.
- **Overexcited Region:** As the field current increases further, the motor starts supplying reactive power, becoming capacitive (Q is negative). This causes the downward slope of the curve.

### Key Points:

- **V-Curve:** Shows the variation of power factor with field current.
- **Inverted V-Curve:** Shows the variation of reactive power with field current.

Understanding these curves is crucial for the operation and control of synchronous motors, as they help in adjusting the excitation to achieve the desired power factor or reactive power compensation.