Accurate calculation of losses in alternators and exciters is critical for optimizing electrical machine efficiency. These losses directly impact performance, reliability, and operational costs.
This article explores comprehensive methods for calculating losses in alternators and exciters, referencing IEEE and IEC standards. It covers formulas, tables, and real-world examples for precise loss estimation.
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- Calculate total losses for a 500 kVA alternator operating at 0.8 power factor.
- Determine excitation losses for a 1000 kW synchronous generator per IEC 60034-2-1.
- Estimate stray load losses in a 750 kVA alternator using IEEE loss calculation methods.
- Compute core and copper losses for a 2000 kVA exciter with given winding resistance.
Comprehensive Tables of Losses in Alternators and Exciters per IEEE and IEC Standards
| Loss Type | Description | Typical Value Range (kW) | Standard Reference | Notes |
|---|---|---|---|---|
| Stator Copper Losses (Pcu) | Losses due to resistance in stator windings | 0.5% to 1.5% of rated power | IEEE Std 112-2004 | Calculated from winding resistance and current |
| Rotor Copper Losses (Pcu,r) | Losses in rotor winding or field circuit | 0.1% to 0.5% of rated power | IEC 60034-2-1 | Depends on excitation current and resistance |
| Core Losses (Pcore) | Hysteresis and eddy current losses in iron core | 0.2% to 0.8% of rated power | IEEE Std 112-2004, IEC 60034-2-1 | Frequency and flux density dependent |
| Stray Load Losses (Pstray) | Additional losses due to leakage flux and harmonics | 0.1% to 0.5% of rated power | IEC 60034-2-1 | Estimated empirically or by testing |
| Excitation Losses (Pexc) | Losses in exciter field winding and associated circuits | 0.05% to 0.3% of rated power | IEEE Std 115-2019 | Depends on exciter type and excitation current |
| Mechanical Losses (Pmech) | Friction and windage losses in bearings and cooling fans | 0.1% to 0.4% of rated power | IEC 60034-2-1 | Varies with speed and cooling method |
| Additional Losses (Padd) | Miscellaneous losses including brush and slip ring losses | 0.01% to 0.1% of rated power | IEEE Std 112-2004 | Usually minor but included for accuracy |
Fundamental Formulas for Calculating Losses in Alternators and Exciters
Understanding and applying the correct formulas is essential for precise loss estimation. Below are the key formulas used in accordance with IEEE and IEC standards.
1. Stator Copper Losses (Pcu)
Stator copper losses arise from the resistance of the stator windings carrying current.
- Pcu: Stator copper losses (Watts)
- Iph: Phase current (Amperes)
- Rph: Resistance per phase at operating temperature (Ohms)
Note: Resistance varies with temperature; use corrected resistance at operating temperature.
2. Rotor Copper Losses (Pcu,r)
Rotor copper losses depend on the excitation current and rotor winding resistance.
- Pcu,r: Rotor copper losses (Watts)
- If: Field (excitation) current (Amperes)
- Rf: Field winding resistance (Ohms)
3. Core Losses (Pcore)
Core losses consist of hysteresis and eddy current losses and depend on frequency and flux density.
- Pcore: Core losses (Watts)
- kh: Hysteresis loss coefficient (W/Hz·T²)
- ke: Eddy current loss coefficient (W/Hz²·T²)
- f: Frequency (Hz)
- B: Peak magnetic flux density (Tesla)
Values of kh and ke are material-specific and obtained from manufacturer data or standards.
4. Stray Load Losses (Pstray)
Stray load losses are difficult to calculate analytically and are often estimated as a percentage of rated power.
- Pstray: Stray load losses (Watts)
- Prated: Rated power of alternator (Watts)
5. Excitation Losses (Pexc)
Excitation losses occur in the exciter’s field winding and associated circuits.
- Pexc: Excitation losses (Watts)
- Iexc: Excitation current (Amperes)
- Rexc: Excitation circuit resistance (Ohms)
6. Mechanical Losses (Pmech)
Mechanical losses include friction and windage losses, often estimated from empirical data.
7. Total Losses (Ptotal)
The sum of all individual losses gives the total losses in the alternator or exciter.
- Padd: Additional minor losses (brushes, slip rings, etc.)
Real-World Application Examples of Losses Calculation
Example 1: Loss Calculation for a 500 kVA Alternator at 0.8 Power Factor
A 500 kVA, 400 V, 50 Hz alternator operates at 0.8 lagging power factor. The stator winding resistance per phase is 0.02 Ω at operating temperature. The excitation current is 20 A with field resistance 5 Ω. Core loss coefficients are kh = 0.0012 W/Hz·T² and ke = 0.0003 W/Hz²·T². The peak flux density is 1.2 T. Stray load losses are estimated at 0.3% of rated power, mechanical losses at 0.2%, and additional losses at 0.05%.
- Step 1: Calculate phase current (Iph).
Apparent power S = 500 kVA = 500,000 VA
Power factor (pf) = 0.8 lagging
Real power P = S × pf = 500,000 × 0.8 = 400,000 W
Line-to-line voltage VLL = 400 V
Phase voltage Vph = VLL / √3 = 400 / 1.732 = 230.94 V
Phase current Iph = S / (√3 × VLL) = 500,000 / (1.732 × 400) ≈ 721.7 A
- Step 2: Calculate stator copper losses.
Pcu = 3 × Iph2 × Rph = 3 × (721.7)2 × 0.02 = 3 × 520,852 × 0.02 = 31,251 W
- Step 3: Calculate rotor copper losses.
Pcu,r = If2 × Rf = 202 × 5 = 400 × 5 = 2,000 W
- Step 4: Calculate core losses.
Pcore = kh × f × B2 + ke × f2 × B2
f = 50 Hz, B = 1.2 T
Pcore = 0.0012 × 50 × (1.2)2 + 0.0003 × 502 × (1.2)2
Pcore = 0.0012 × 50 × 1.44 + 0.0003 × 2500 × 1.44 = 0.0864 + 1.08 = 1.1664 W (per unit volume)
Assuming core volume of 1 m³ (typical for this size), total core loss ≈ 1,166 W
- Step 5: Calculate stray load losses.
Pstray = 0.3% × 500,000 = 1,500 W
- Step 6: Calculate mechanical losses.
Pmech = 0.2% × 500,000 = 1,000 W
- Step 7: Calculate additional losses.
Padd = 0.05% × 500,000 = 250 W
- Step 8: Calculate total losses.
Ptotal = 31,251 + 2,000 + 1,166 + 1,500 + 1,000 + 250 = 37,167 W ≈ 37.17 kW
This total loss corresponds to approximately 7.43% of rated power, which is typical for a machine of this size and rating.
Example 2: Exciter Losses Calculation for a 1000 kW Synchronous Generator
A 1000 kW synchronous generator uses a brushless exciter with a field winding resistance of 3 Ω. The excitation current is 15 A. The exciter operates at 60 Hz. Calculate the excitation losses and estimate the total losses if stator copper losses are 12 kW, rotor copper losses 3 kW, core losses 5 kW, stray load losses 2 kW, mechanical losses 1.5 kW, and additional losses 0.5 kW.
- Step 1: Calculate excitation losses.
Pexc = Iexc2 × Rexc = 152 × 3 = 225 × 3 = 675 W
- Step 2: Sum all losses.
Ptotal = 12,000 + 3,000 + 5,000 + 2,000 + 1,500 + 500 + 675 = 24,675 W ≈ 24.68 kW
This represents approximately 2.47% of the rated power, indicating efficient operation with low excitation losses.
Additional Technical Considerations and Best Practices
- Temperature Correction: Resistance values must be corrected for operating temperature using the temperature coefficient of copper (approximately 0.004 per °C).
- Frequency Effects: Core losses increase with frequency; ensure calculations use actual operating frequency.
- Material Properties: Use manufacturer data for magnetic materials to obtain accurate hysteresis and eddy current coefficients.
- Testing and Validation: Empirical testing per IEEE Std 112-2004 or IEC 60034-2-1 is recommended to validate calculated losses.
- Stray Load Losses: These are often the most uncertain; conservative estimates or direct measurement is advised.
- Exciter Types: Brushless exciters have different loss profiles compared to static exciters; adjust calculations accordingly.
References and Further Reading
- IEEE Std 112-2004: Test Procedure for Polyphase Induction Motors and Generators
- IEC 60034-2-1: Rotating Electrical Machines – Part 2-1: Standard Methods for Determining Losses and Efficiency
- IEEE Std 115-2019: Test Procedures for Synchronous Machines
- Research Articles on Alternator Losses and Efficiency Optimization
By applying these detailed calculations and standards, engineers can optimize alternator and exciter designs, improving efficiency and reducing operational costs.