SSC JE Power System Questions with Detailed Solutions

$$\textbf{Given:} \\[6pt]\bullet \; \text{Power transmitted } (P_0) = 1,100 \, kW \\\bullet \; \text{Voltage } (V) = 11 \, kV = 11,000 \, V \\\bullet \; \text{Resistance } (R) = 5 \, \Omega \\\bullet \; \text{Power factor } = 1 \, (\text{Unity}) \\[12pt]\textbf{Formula Used:} \\[6pt]\bullet \; \text{Current } (I) = \dfrac{P_0}{V} \\[10pt]\bullet \; \text{Power loss } (P_{loss}) = I^2 R \\[10pt]\bullet \; \text{Input power } (P_{in}) = P_0 + P_{loss} \\[10pt]\bullet \; \text{Efficiency } (\eta) = \dfrac{P_0}{P_{in}} \times 100 \\[12pt]\textbf{Solution:} \\[6pt]\text{Current:}$$​​

$$I = \dfrac{1,100,000}{11,000} = 100 \, A \\[12pt]\text{Power loss:} \\P_{loss} = (100)^2 \times 5 = 50 \, kW \\[12pt]\text{Input power:} \\P_{in} = 1,100 \, kW + 50 \, kW = 1,150 \, kW \\[12pt]\text{Efficiency:} \\\eta = \dfrac{1,100}{1,150} \times 100 = 95.65\%$$​​

A ring main distribution system is preferred over a radial distribution system because in a ring system, power can flow in both directions from a transformer, meaning if a fault occurs on one section of the ring, the power can still reach consumers through the other section, minimizing voltage fluctuations at consumer terminals due to the redundancy in the circuit. 

A radial distribution network is most suitable when the substation is located near the load center because it minimizes voltage drops and line losses due to the short transmission distance. 
Additionally, low voltage generation is also favorable for radial systems as they are simple and cost-effective at lower voltage levels. Placing the substation at the load center further enhances these advantages. 

 In a ring main AC distribution system, power factor significantly impacts the voltage drop between the sending and receiving ends. 
 Power factor represents the efficiency of how electrical power is utilized. A lower power factor indicates greater reactive power flow, which leads to increased voltage drop along the circuit. 
 This is because the current flowing through the system is higher for the same amount of real power delivered. 
 Therefore, power factor is a crucial consideration in determining the voltage regulation within a ring main network. 

$$\textbf{Given:} \\[6pt]\bullet \; \text{Power transmitted } (P_0) = 1,100 \, kW \\\bullet \; \text{Voltage } (V) = 11 \, kV = 11,000 \, V \\\bullet \; \text{Resistance } (R) = 5 \, \Omega \\\bullet \; \text{Power factor } = 1 \, (\text{Unity}) \\[12pt]\textbf{Formula Used:} \\[6pt]\bullet \; \text{Current } (I) = \dfrac{P_0}{V} \\[10pt]\bullet \; \text{Power loss } (P_{loss}) = I^2 R \\[10pt]\bullet \; \text{Input power } (P_{in}) = P_0 + P_{loss} \\[10pt]\bullet \; \text{Efficiency } (\eta) = \dfrac{P_0}{P_{in}} \times 100 \\[12pt]\textbf{Solution:} \\[6pt]\text{Current:}$$​​

$$I = \dfrac{1,100,000}{11,000} = 100 \, A \\[12pt]\text{Power loss:} \\P_{loss} = (100)^2 \times 5 = 50 \, kW \\[12pt]\text{Input power:} \\P_{in} = 1,100 \, kW + 50 \, kW = 1,150 \, kW \\[12pt]\text{Efficiency:} \\\eta = \dfrac{1,100}{1,150} \times 100 = 95.65\%$$​​

In a radial distribution network, power flows from the substation to the consumers, with each consumer connected along a single feeder. As electricity travels through the conductor, it encounters resistance, causing a voltage drop. This means that consumers further away from the substation experience a larger voltage drop compared to those closer, resulting in more significant voltage fluctuations. 

The diversity factor is a measure of the non-coincidence of peak demands among multiple consumers.
It is given by:

$$\text{Diversity Factor} = \dfrac{\text{Sum of individual maximum demands}}{\text{Maximum demand of the system (power station)}}$$​

 Since all consumers do not peak at the same time, the system's peak is less than the sum of individual peaks.
 Therefore, diversity factor is always ≥1.

An earth fault relay is designed to detect small faults to the ground, which are typically much smaller than the normal load current. If the relay setting was equal to or greater than the load current, it wouldn't trip for small earth faults, defeating its purpose. Therefore, the setting needs to be significantly lower to ensure quick detection and isolation of earth faults. 

Cold reserve capacity refers to a backup power source that is available but not actively generating electricity, meaning it can be quickly activated when needed, unlike "hot reserve" which is readily available and online. 

In a ring main distribution system, the primary windings of multiple distribution transformers are connected in a loop, forming a closed circuit that allows electricity to flow through the network. 

When the receiving end voltage is greater than the sending end voltage, it is known as the Ferranti effect. This occurs in lightly loaded or open-circuited long transmission lines due to the effect of line capacitance.
The mathematical condition for this phenomenon under leading power factor load is:

This inequality indicates that the drop due to reactance dominates over that due to resistance, leading to the voltage rise at the receiving end.

Cold reserve refers to the reserve capacity of a plant that is available for service (meaning it can be brought online if needed) but is not currently in operation. It is important to distinguish between "cold reserve" and "hot reserve": 
Cold reserve: This capacity is not actively generating power but can be readily started up when needed. Think of it like a car parked in the driveway that's ready to go on a trip but is currently not running.
Hot reserve: This capacity is already running and connected to the grid but is not currently being used to its full potential. Imagine a car running at a low speed on the highway, ready to accelerate if needed. It's in service and contributing to the overall power supply, but not operating at full capacity.

Power factor and efficiency: In AC power transmission, a higher power factor means less reactive power is drawn, which translates to less losses in the transmission line, thereby increasing efficiency. 
Leading power factor: When the power factor is slightly less than unity and leading, the load is essentially supplying reactive power back to the grid, further reducing losses and improving efficiency. 
Lagging power factor: Conversely, a lagging power factor indicates the load is drawing reactive power from the grid, causing increased losses. 
Unity power factor: While a unity power factor (PF=1) means no reactive power is present, slight variations slightly less than unity leading are considered optimal for practical reasons. 

DFIG function: A DFIG allows the wind turbine to operate at variable speeds by controlling the rotor frequency, which is achieved by adjusting the power supplied to the rotor windings through the back-to-back converter.
Back-to-back converter role: This converter essentially acts as a bridge between the rotor and the grid, allowing for variable frequency power to be injected into the rotor, thereby controlling the turbine's speed and power output. 

In India, ethanol is primarily produced from sugarcane molasses, a by-product of sugar production. While other crops like corn can be used for ethanol production globally, sugarcane is the dominant feedstock in India.