Three-Phase & Single-Phase Power Systems: Star & Delta Connections Explained

Posted on Jun 27, 2024 in Electronics

Three-Phase Electric Power

• Single-Phase System: Two wires (phase and neutral) carry current.
• Three-Phase System: Three wires carry AC voltages, making it more economical than a single-phase system.

Star (Y) and Delta (Δ) Connections

• Star Connection:

  • Structure: 4 wires (3 phases, 1 neutral).
  • Voltage: Each winding receives 230V.
  • Applications: Power transmission for longer distances, requires less starting current.
  • Insulation: Less insulation is needed due to different line and phase voltages (VL = √3 VP).
  • Power Calculation: P = 3 x VP x IP x Cos(Φ) or P = √3 x VL x IL x Cos(Φ).
  • Advantages: Versatility in voltage levels, used in both transmission and distribution networks.

• Delta Connection:

  • Structure: 3 wires (all phases).
  • Voltage: Each winding receives 415V.
  • Applications: Power distribution for shorter distances, requires high starting torque.
  • Insulation: More insulation is needed as line and phase voltages are the same (VL = VP).
  • Power Calculation: P = 3 x VP x IP x Cos(Φ) or P = √3 x VL x IL x Cos(Φ).
  • Advantages: Simplicity in voltage levels, used primarily in distribution networks.

Comparison

• Voltage: Star provides dual voltage levels, while Delta offers a single voltage.
• Current: In Star, line current equals phase current (IL = IP). In Delta, line current is root three times phase current (IL = √3 IP).
• Applications: Star is suitable for longer distances and requires less starting current; Delta is suitable for shorter distances and requires high starting torque.

Usage in Networks

• Star Connection: Common in both transmission and distribution networks for flexibility and efficiency.
• Delta Connection: Common in distribution networks for simplicity and high torque requirements.

Key Takeaways

• Economy and Efficiency: Three-phase systems are more economical for power transmission.
• Application Suitability: The choice of Star or Delta connection depends on distance and current requirements.
• Insulation and Voltage: Different insulation needs are based on voltage differences in the connections.

Working Principle of a Single-Phase Transformer

Question 3: Explain the Working of a PMMC Instrument

Working of a Permanent Magnet Moving Coil (PMMC) Instrument:

• PMMC instruments work on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a force.
• The moving coil is placed in the uniform magnetic field of a permanent magnet.
• When current passes through the coil, it experiences a torque due to the magnetic field.
• This torque causes the coil to rotate, and the pointer attached to the coil moves over a calibrated scale to give the measurement.
• The deflection of the pointer is proportional to the current flowing through the coil.
• A spring provides a controlling torque that balances the deflecting torque when the pointer is at its final position.

Question 4: Explain the Working Principle of a PMMI Instrument

Working of a Permanent Magnet Moving Iron (PMMI) Instrument:

• PMMI instruments operate on the principle that when a piece of soft iron is placed in the magnetic field of a permanent magnet, it gets magnetized and experiences a force.
• This force causes the iron piece to move, which in turn moves the pointer over a calibrated scale.
• The deflection of the pointer is proportional to the current passing through the coil that produces the magnetic field.
• The moving iron instrument can be of two types: attraction type and repulsion type.
• In the attraction type, a piece of iron is attracted towards the coil when current flows through it.
• In the repulsion type, two pieces of iron are magnetized similarly and repel each other when current flows through the coil.

Question 5: Explain Waveforms and Expressions in AC Circuits

Waveforms:

• In a pure resistive circuit, voltage and current are in phase.
• In a pure inductive circuit, the current lags the voltage by 90 degrees.
• In an RL circuit, the current lags the voltage by an angle ϕ where tan(ϕ) = XL/R.
• In an RC circuit, the current leads the voltage by an angle ϕ where tan(ϕ) = 1/ωCR.
• In an RLC circuit, the phase angle depends on the relative values of resistance, inductance, and capacitance, with the current either leading or lagging the voltage depending on whether the circuit is inductive or capacitive.

Expressions:

• Pure Resistance (R):

  • Voltage: V(t) = Vmsin(ωt)
  • Current: I(t) = Imsin(ωt)
  • Here, Vm and Im are the maximum voltage and current, respectively, and ω is the angular frequency.

• Pure Inductance (L):

  • Voltage: V(t) = Vmsin(ωt)
  • Current: I(t) = Imsin(ωt – 90°) = Imsin(ωt – π/2)
  • The current lags the voltage by 90 degrees.

• RL Circuit (Resistor and Inductor in series):

  • Voltage: V(t) = Vmsin(ωt)
  • Current: I(t) = Imsin(ωt – ϕ)
  • The phase angle ϕ is given by tan(ϕ) = XL/R = ωL/R.

• RC Circuit (Resistor and Capacitor in series):

  • Voltage: V(t) = Vmsin(ωt)
  • Current: I(t) = Imsin(ωt + ϕ)
  • The phase angle ϕ is given by tan(ϕ) = 1/ωCR.

• RLC Circuit (Resistor, Inductor, and Capacitor in series):

  • Voltage: V(t) = Vmsin(ωt)
  • Current: I(t) = Imsin(ωt – ϕ)
  • The phase angle ϕ is given by tan(ϕ) = (XL – XC)/R = (ωL – 1/ωC)/R.

Waveforms and Explanations:

1. Pure Resistance (R):

   • The voltage and current waveforms are sinusoidal and in phase.
   • Power P(t) = V(t) ⋅ I(t) = VmImsin²(ωt), which is always positive and oscillates with double the frequency of the voltage/current waveforms.

2. Pure Inductance (L):

   • The current waveform lags the voltage waveform by 90 degrees.
   • Power P(t) = V(t) ⋅ I(t) alternates between positive and negative values, with an average power of zero over a full cycle.

3. RL Circuit:

   • The current waveform lags the voltage waveform by a phase angle ϕ.
   • Power P(t) = V(t) ⋅ I(t) has both positive and negative values but with a net positive average power over a cycle due to the resistive component.

4. RC Circuit:

   • The current waveform leads the voltage waveform by a phase angle ϕ.
   • Power P(t) = V(t) ⋅ I(t) behaves similarly to the RL circuit, but the phase relationship is different.

5. RLC Circuit:

   • The current waveform either leads or lags the voltage waveform depending on whether the circuit is capacitive or inductive.
   • Power P(t) = V(t) ⋅ I(t) varies depending on the relative magnitudes of R, L, and C, with a net positive average power over a cycle if the circuit is not purely reactive.

Section A

1. Classify and Describe Electrical Elements Based on Linearity:

   • Linear Elements: These elements have a linear relationship between voltage and current. Examples include resistors, inductors, and capacitors.
   • Non-linear Elements: These elements do not have a linear relationship between voltage and current. Examples include diodes, transistors, and varistors.

2. Classify Dependent Sources and Describe Each Type:

   • Voltage-Controlled Voltage Source (VCVS): A voltage source whose output voltage is proportional to a controlling voltage elsewhere in the circuit.
   • Voltage-Controlled Current Source (VCCS): A current source whose output current is proportional to a controlling voltage elsewhere in the circuit.
   • Current-Controlled Voltage Source (CCVS): A voltage source whose output voltage is proportional to a controlling current elsewhere in the circuit.
   • Current-Controlled Current Source (CCCS): A current source whose output current is proportional to a controlling current elsewhere in the circuit.

3. Mathematical Expression for a 50 Hz Sinusoidal Voltage:

   The mathematical expression for a sinusoidal voltage can be written as: v(t) = Vmsin(ωt + ϕ).

   For a 50 Hz frequency and 230 V RMS voltage: Vm = 230√2, ω = 2π × 50, v(t) = 230√2sin(2π × 50t).

4. Phasor Diagram and Power Factor for a Series R-L Circuit:

   • Phasor Diagram:

     • The voltage across the resistor (VR) is in phase with the current (I).
     • The voltage across the inductor (VL) leads the current (I) by 90 degrees.
     • The total voltage (V) is the vector sum of VR and VL.

   • Power Factor: cos(ϕ) = R/Z, where Z = √(R² + (XL)²) and XL = ωL.

5. Classify DC Machines:

   • Based on Excitation:
     • Self-excited
     • Separately excited
   • Based on Construction:
     • Series
     • Shunt
     • Compound

6. Classify DC Motors:

   • Shunt Motor
   • Series Motor
   • Compound Motor

7. Importance of Earthing:

   • Safety: Prevents electric shock.
   • Protection: Protects electrical appliances and circuits.
   • Fault Management: Helps in fault detection and isolation.

8. Differentiate Between PMMC and Moving Iron Instruments:

   • PMMC (Permanent Magnet Moving Coil):

     • Linear scale
     • High accuracy
     • Used for DC measurements

   • Moving Iron:

     • Non-linear scale
     • Less accurate than PMMC
     • Used for both AC and DC measurements

Section B

2. a. Draw and Explain the VI Graph of:

   • Ideal Resistor: Linear relationship (Ohm’s Law: V = IR).
   • Ideal Inductor: Voltage leads current by 90 degrees.
   • Ideal Capacitor: Current leads voltage by 90 degrees.
   • Ideal Voltage Source: Provides constant voltage irrespective of current.
   • Ideal Current Source: Provides constant current irrespective of voltage.
   • Wire: Ideal conductor, negligible resistance, V ≈ 0V.

3. b. Use Source Conversion Technique to Find Voltage V0 of the Circuit:

   (Circuit conversion steps need to be shown with necessary calculations.)

4. c. Find the Current Flowing Through the 10Ω Resistance Using the Superposition Theorem:

   (Apply Superposition Theorem steps with necessary calculations.)

Section C

3. a. Derive the Expression for Instantaneous Sinusoidal EMF:

   e(t) = Emsin(ωt + ϕ)

4. b. Explain with Diagrams: In Phase, Lagging, and Leading in Sinusoidal Quantities:

   • In Phase: Voltage and current waveforms cross zero at the same time.
   • Lagging: Current waveform lags behind the voltage waveform.
   • Leading: Current waveform leads the voltage waveform.

5. c. Analyze the Alternating Voltage v = 141.4sin(314t):

   • Frequency (f):

   • RMS Value:

   • Average Value:

   • Instantaneous Value of Voltage when t = 3 ms:

   • Time Taken for Voltage to Reach 100 V for the First Time After Passing Through Zero Value:

6. 4. Attempt Any Two:

   (a) Classify Transformers Based on:

   Classification of Transformers:

   Transformers can be classified according to several factors:

   (i) Number of Windings:

   • Two-winding transformers: These transformers have a primary winding and a secondary winding. The primary winding is connected to the input voltage source, and the secondary winding supplies power to the load.
   • Autotransformers: These transformers have a single winding with a tapped section. The voltage at the tap point is used as the secondary voltage.

   (ii) Number of Phases:

   • Single-phase transformers: These transformers are used in single-phase power systems. They have a primary winding designed for a single-phase AC voltage and a secondary winding that can be designed for either a single-phase or a multiple-phase (e.g., three-phase) output.
   • Three-phase transformers: These transformers are used in three-phase power systems. They have a primary winding designed for three-phase AC voltage and a secondary winding that can be designed for either a three-phase or a single-phase output.

   (iii) Voltage Levels:

   • Step-up transformers: These transformers increase the voltage level from the primary winding to the secondary winding.
   • Step-down transformers: These transformers decrease the voltage level from the primary winding to the secondary winding.
   • Isolation transformers: These transformers isolate the secondary circuit from the primary circuit while maintaining the same voltage level.

Working of a Single-Phase Transformer (with Diagram)

A single-phase transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It typically consists of two windings (primary and secondary) wound around a common iron core. Here’s an explanation of its working, followed by a neat diagram:

Working Principle of a Single-Phase Transformer

1. Primary Winding: The transformer receives AC voltage from the supply on the primary winding. When AC voltage is applied to the primary winding, it creates an alternating magnetic field around the winding.

2. Magnetic Core: The alternating magnetic field created in the primary winding is concentrated by the magnetic core, usually made of laminated iron to minimize energy loss.

3. Induced EMF: This alternating magnetic field induces an electromotive force (EMF) in the secondary winding according to Faraday’s Law of Electromagnetic Induction. The amount of voltage induced in the secondary winding depends on the turns ratio between the primary and secondary windings.

4. Secondary Winding: The induced voltage in the secondary winding provides the output voltage to the load connected to it. The voltage can be stepped up or stepped down depending on the turns ratio of the transformer.

Types of Earthing (with Diagram of Pipe Earthing)

Types of Earthing

Earthing (or grounding) is a critical aspect of electrical systems, ensuring safety and preventing electrical shocks. There are several types of earthing methods used to achieve this:

1. Plate Earthing
2. Pipe Earthing
3. Rod Earthing
4. Strip Earthing
5. Earthing through Water Mains

Pipe Earthing

Pipe earthing is one of the most common and effective methods used for grounding electrical installations. It involves burying a galvanized steel pipe vertically into the ground to provide a low-resistance path to earth. Here is a detailed explanation and a neat diagram illustrating the pipe earthing system.

Components of Pipe Earthing

1. Earthing Pipe: A galvanized steel pipe with perforations to increase contact with the soil.
2. Earth Wire: A wire connected to the earthing system, linking the installation to the earth pipe.
3. Moisture Retaining Compound: Surrounds the pipe to maintain moisture and reduce resistance.
4. Earthing Pit: A pit in which the earthing pipe is buried.
5. Charcoal and Salt: Used to maintain moisture and improve conductivity around the pipe.

Procedure

1. Digging the Pit: A pit about 2.5 to 3 meters deep and about 30 cm in diameter is dug.
2. Placement of the Pipe: A galvanized steel pipe (typically 2.5 to 3 meters in length and 38 mm in diameter) is placed vertically in the pit.
3. Filling with Charcoal and Salt: The pit is filled with layers of charcoal and salt to maintain soil moisture and improve conductivity.
4. Connecting the Earth Wire: The earth wire from the installation is securely connected to the top of the earthing pipe using a bolt or clamp.
5. Covering the Pit: The pit is then covered with soil, leaving a small portion of the pipe above ground for easy access.

Diagram of Pipe Earthing

(Please note that you will need to add the actual diagrams for the phasor diagram, VI graphs, circuit diagrams, and the pipe earthing diagram as I cannot generate images in this text-based format.)