An Alternator, also known as a Synchronous Generator, is used to convert mechanical energy into electrical energy in the form of alternating current (AC). The key phenomenon behind this is Electromagnetic Induction. In this blog, we will understand the concept, derivation, and formula of EMF induced in an alternator, along with quick memory tips useful for exams like SSC JE, RRB JE, GATE, and UPPCL JE.
⚙️ Basic Concept of EMF Induction in Alternator
When the rotor of an alternator rotates, its magnetic field cuts the stationary armature windings placed on the stator. According to Faraday’s Law of Electromagnetic Induction, an electromotive force (EMF) is induced in the stator conductors.
- Rotor: Contains field winding, supplied with DC.
- Stator: Contains armature winding, where AC EMF is induced.
- Rotation: Rotor rotates at synchronous speed (Ns = 120f/P).
🧮 Formula for EMF Induced in Alternator (RMS Value)
The RMS value of the EMF induced per phase in an alternator is given by the equation:
E = 4.44 × f × Φ × T × Kp × Kd
Where:
- E = RMS value of induced EMF per phase
- f = Frequency in Hz
- Φ = Flux per pole in Weber (Wb)
- T = Number of turns per phase
- Kp = Pitch factor (or coil span factor)
- Kd = Distribution factor
🧠 Detailed Derivation of EMF Equation in Alternator
Let’s derive the equation for the RMS value of EMF induced per phase in a 3-phase alternator based on Faraday's laws of electromagnetic induction.
1️⃣ Let us assume:
- P = Number of poles
- N = Rotor speed in RPM
- f = Frequency of generated EMF in Hz
- Φ = Flux per pole in Weber
- Z = Total number of conductors per phase
- T = Number of turns per phase = Z/2
- Kp = Pitch factor
- Kd = Distribution factor
2️⃣ Frequency of generated EMF:
Each conductor is cut by P poles in one revolution of the rotor. If the rotor rotates at N RPM, then:
f = (P × N) / 120
3️⃣ Average EMF induced in one conductor:
By Faraday’s law, the average EMF induced in one conductor = Rate of change of flux = dΦ/dt.
In one revolution, a conductor is cut by P × Φ weber of flux in 60/N seconds.
Average EMF in one conductor = (P × Φ) / (60 / N) = (P × Φ × N) / 60
4️⃣ Average EMF per phase:
Total conductors per phase = Z
Total turns per phase = T = Z / 2
So, average EMF per phase = EMF in one conductor × number of conductors
Eavg = (P × Φ × N × Z) / 60 = (P × Φ × N × 2T) / 60
5️⃣ RMS value of generated EMF per phase:
For a sinusoidal waveform, RMS value is:
E = Form Factor × Eavg
Form factor = 1.11 for sine wave
E = 1.11 × (P × Φ × N × 2T) / 60
Simplify the constants:
E = 4.44 × f × Φ × T
6️⃣ Include pitch and distribution factors:
In practical alternators, windings are not full-pitched or concentrated. So, the actual induced EMF is reduced due to:
- Pitch factor (Kp): accounts for short-pitch coils
- Distribution factor (Kd): accounts for distributed winding over slots
Therefore, final EMF equation becomes:
E = 4.44 × f × Φ × T × Kp × Kd
✅ Summary:
- EMF is directly proportional to flux, frequency, and number of turns.
- Kp and Kd always < 1 → reduce EMF slightly due to winding design.
- This equation gives the RMS value of generated EMF per phase in a 3-phase alternator.
🧠 Simplified form Derivation
- The rotor produces a flux Φ per pole.
- In one revolution, flux cuts the stator coils.
- Number of poles = P, speed = N RPM
- So, frequency f = (P × N) / 120
- Average EMF = P × Φ × N × T / 60
- Convert to RMS and include form factor & winding factors:
RMS EMF per phase: E = 4.44 × f × Φ × T × Kp × Kd
🔍 Factors Affecting Induced EMF
- Flux (Φ): Directly proportional
- Speed: Affects frequency f = PN/120
- Number of turns (T): Higher turns = higher EMF
- Kp & Kd: Corrected for winding design
✍️ Short Notes to Remember (Exam Tips)
- Always remember the base formula: E = 4.44 f Φ T (ideal case)
- Kp < 1 (due to short-pitching), Kd < 1 (due to distributed winding)
- Max EMF → Full pitch & concentrated winding
- Reducing harmonics → Short pitch + Distributed winding
- For quick estimation, remember: E ∝ f × Φ × N
⚡ Numerical Example
Example: A 3-phase alternator has 4 poles and runs at 1500 RPM. It has 60 turns per phase, flux per pole = 0.05 Wb. The pitch factor Kp = 0.95, distribution factor Kd = 0.96. Find the RMS value of induced EMF per phase.
Solution:
- f = (P × N) / 120 = (4 × 1500) / 120 = 50 Hz
- E = 4.44 × f × Φ × T × Kp × Kd
- E = 4.44 × 50 × 0.05 × 60 × 0.95 × 0.96 = 606.8 V
Answer: 606.8 V (per phase)
📌 Important Points for MCQs
- Standard frequency in India = 50 Hz
- Higher flux → higher EMF
- Pitch factor Kp = cos(α/2), α = angle of short pitching
- Distribution factor Kd = sin(mβ/2)/(m sin(β/2))
❓ FAQs – EMF in Alternator
Q1. Why is EMF induced in the stator, not the rotor?
Because the stator is stationary and easier to tap AC output from it, while the rotor is supplied with DC field current.
Q2. What are the units of EMF?
Volts (V).
Q3. What is the significance of Kp and Kd?
They correct the theoretical EMF for practical winding arrangements (short pitch & distributed).
Q4. What is the effect of increasing rotor speed?
Increases frequency, hence increases induced EMF.
Q5. What is the full-pitch winding?
A winding in which coil span = pole pitch, so Kp = 1.