Energy Audit & Management (EX-703 (B)) - Unit 5 Short Notes

UNIT 5: ENERGY AUDIT & MANAGEMENT - SHORT NOTES

A. FOUNDATIONS OF ENERGY AUDITING & MANAGEMENT

Definition, Need, and Scope of Energy Audit

• Definition: A systematic procedure to evaluate an organization's energy consumption, identify areas of energy wastage, and recommend measures for conservation and efficiency improvement. It is the first step towards rational energy use.

• Need: Rising energy costs, environmental concerns (carbon footprint), energy security, regulatory compliance (BEE), and operational efficiency.

• Scope: Covers all energy forms (electrical, thermal, fuel) across all utilities (boilers, HVAC, pumps, lighting, compressors) and processes.

Types of Energy Audits (High Frequency)

Distinction: Preliminary is qualitative & quick; Detailed is quantitative & thorough.

Energy Manager: Roles, Duties, and Responsibilities (High Frequency)

• Roles: Planner, organizer, motivator, controller.

• Duties:

  1. Develop & implement energy policy.

  2. Coordinate energy audit teams.

  3. Collect & analyze energy data.

  4. Identify & prioritize Energy Conservation Opportunities (ECOs).

  5. Prepare technical & financial reports.

  6. Train staff & promote awareness.

  7. Monitor & verify savings post-implementation.

  8. Ensure compliance with BEE regulations.

General Principles and Functions of Energy Management

• Principles: Top management commitment, continuous improvement, measurement & verification, life-cycle costing, employee involvement.

• Functions (PDCA Cycle):

  1. Plan: Set policy, objectives, baseline.

  2. Do: Implement ECOs, train.

  3. Check: Monitor, measure, verify savings.

  4. Act: Review, improve, re-plan.

Barriers to Energy Auditing and their Elimination

Manners and Intervals for Conduct of Energy Audit as per BEE Regulations (High Frequency)

• Manners: Conducted by Certified Energy Auditors (CEA) or Certified Energy Managers (CEM). Must follow BEE's "Energy Audit – A Guide" methodology. Includes data collection, walk-through, measurements, analysis, reporting.

• Intervals (for Designated Consumers - DCs):

  • First Audit: Within 3 years of being notified as DC.

  • Subsequent Audits: Every 5 years from the date of the previous audit report submission to BEE.

  • Compliance: Submit audit report to BEE within 6 months of audit completion.

B. ENVIRONMENTAL ASPECTS

Environmental Aspects of Energy Consumption (High Frequency)

Elements of Systematic Environmental Assessment

1. Goal & Scope Definition: Boundaries (cradle-to-gate), functional unit.

2. Inventory Analysis (LCI): Quantify all material/energy inputs & emissions.

3. Impact Assessment (LCIA): Classify & characterize impacts (Global Warming Potential, Acidification, etc.).

4. Interpretation: Identify hotspots, sensitivity analysis, conclusions.

C. ELECTRICAL SYSTEMS & POWER QUALITY

Power Factor (PF) Improvement (Very High Frequency)

• Definition: PF = $$\displaystyle \frac{\text{Real Power (kW)}}{\text{Apparent Power (kVA)}} = \cos\phi $$. It measures effective utilization of electrical power.

• Need for Improvement: Low PF (lagging) increases current for same kW, leading to:

  • Higher kVA demand → higher fixed charges.

  • Increased I²R losses in cables/transformers.

  • Voltage drop → poor performance.

  • Penalty from utility.

• Correction using Capacitor Banks: Capacitors supply leading kVAr, neutralizing lagging kVAr from inductive loads (motors).

  • New kVA after correction: $$\displaystyle \text{kVA}_{\text{new}} = \sqrt{(\text{kW})^2 + (\text{kVAr}_{\text{old}} - \text{kVAr}_{\text{cap}})^2} $$

  • kVAr required: $$\displaystyle \text{kVAr}_{\text{cap}} = \text{kW} \left( \tan\phi_1 - \tan\phi_2 \right) $$

    where $$\displaystyle \phi_1 = \cos^{-1}(\text{PF}_{\text{old}}) $$, $$\displaystyle \phi_2 = \cos^{-1}(\text{PF}_{\text{new}}) $$.

• Best Location (Energy Conservation Perspective):

  1. Individual Motor Terminals (Most Effective): Reduces current in entire upstream circuit (cable, panel, transformer). Saves losses everywhere.

  2. Main Distribution Board/Sub-station: Easier to install, but does not save losses in individual branch circuits.

  Golden Rule: Install capacitors as close as possible to the inductive load.

Penalty Calculation Problem (Typical)

• Given: Max Demand (kVA), Avg PF, Min Required PF, Penalty per % dip.

• Steps:

  1. Calculate existing lagging kVAr: $$\displaystyle \text{kVAr}_{\text{old}} = \text{kVA} \times \sin(\cos^{-1}(\text{PF}_{\text{old}})) $$

  2. Calculate target kVAr: $$\displaystyle \text{kVAr}_{\text{new}} = \text{kVA} \times \sin(\cos^{-1}(\text{PF}_{\text{min}})) $$

  3. kVAr to be injected: $$\displaystyle \text{kVAr}_{\text{cap}} = \text{kVAr}_{\text{old}} - \text{kVAr}_{\text{new}} $$

  4. Improved PF after installing kVAr_cap: $$\displaystyle \text{PF}_{\text{improved}} = \cos\left[\tan^{-1}\left(\frac{\text{kVAr}_{\text{old}} - \text{kVAr}_{\text{cap}}}{\text{kW}}\right)\right] $$

  5. % Dip = $$\displaystyle (\text{PF}_{\text{min}} - \text{PF}_{\text{improved}}) \times 100 $$

  6. Penalty = % Dip × Penalty Rate.

Harmonics (High Frequency)

• Definition: Sinusoidal components with frequencies that are integer multiples of the fundamental frequency (50 Hz). Caused by non-linear loads.

• Major Problems:

  • Overheating of transformers, motors, cables (due to additional eddy current & hysteresis losses).

  • Nuisance tripping of protective devices (MCBs, RCCBs).

  • Capacitor failure (resonance, overloading).

  • Malfunction of sensitive electronics (computers, PLCs).

  • Neutral conductor overheating in 3-phase 4-wire systems (triplen harmonics add in neutral).

• Equipment Contributing to Harmonics:

  • Static Sources: SMPS, computers, LED drivers, electronic ballasts.

  • Rotating Machines: Saturation in transformers/induction motors.

  • Arcing Devices: Welding machines, arc furnaces, fluorescent lamps.

  • Power Electronics: AC/DC drives (VFDs), rectifiers, inverters.

• Harmonic Distortion Evaluation:

  1. Measure voltage/current waveforms with Power Quality Analyzer.

  2. Perform FFT (Fast Fourier Transform) to decompose into harmonic components.

  3. Calculate Total Harmonic Distortion (THD):

$$ \text{THD}_V (\%) = \frac{\sqrt{\sum_{h=2}^{40} V_h^2}}{V_1} \times 100 $$

$$ \text{THD}_I (\%) = \frac{\sqrt{\sum_{h=2}^{40} I_h^2}}{I_1} \times 100 $$

    where subscript `1` = fundamental, `h` = harmonic order.

Energy Efficient Motors vs. Standard Motors (High Frequency)

Motor Loading Calculation from Input (V, I, PF)

• Given: Input Voltage (V), Input Current (I), Power Factor (PF), Full Load Efficiency ($$\displaystyle \eta_{\text{FL}} $$), Rated Power (P_rated).

• Steps:

  1. Calculate Input Power (kW): $$\displaystyle P_{\text{in}} = \sqrt{3} \times V \times I \times \text{PF} / 1000 $$

  2. Calculate Output Power (kW): $$\displaystyle P_{\text{out}} = P_{\text{in}} \times \eta_{\text{actual}} $$

     • Note: $$\displaystyle \eta_{\text{actual}} $$ is unknown. Approximate using full-load efficiency if load is >75%, or use typical part-load efficiency curves.

  3. % Loading = $$\displaystyle \frac{P_{\text{out}}}{P_{\text{rated}}} \times 100 $$

  Common Pitfall: Using input power directly without accounting for efficiency. Output power = Input power × Efficiency.

Transformer Losses and Minimization

• Losses:

  • Core (Iron) Losses: Constant, depend on voltage & frequency. Hysteresis & Eddy currents.

  • Copper (I²R) Losses: Variable, depend on load current².

• Minimization:

  • Core: Use high-grade, thin, insulated silicon steel (CRGO). Amorphous metal cores (much lower).

  • Copper: Use larger conductor cross-section (higher cost, lower loss).

  • Design: Optimize flux density, minimize stray losses.

  • Operation: Avoid overloading, maintain good cooling, ensure good power quality (minimize harmonics).

D. THERMAL SYSTEMS & BOILERS

Boiler Efficiency (High Frequency)

• Direct Method (Input-Output):

$$ \eta_{\text{direct}} (\%) = \frac{\text{Steam Output (kg/hr)} \times (\text{Enthalpy of Steam} - \text{Enthalpy of Feedwater})}{\text{Fuel Input (kg/hr)} \times \text{GCV}} \times 100 $$

*   **Pros:** Simple, quick.

*   **Cons:** Does not identify *why* losses occur.

• Indirect Method (Losses Method):

$$ \eta_{\text{indirect}} (\%) = 100 - (\text{Sum of all % losses}) $$

**Major Losses:**

1.  **Loss due to dry flue gas:** $$\displaystyle \frac{m_{\text{fg}} \times C_p \times (T_{\text{fg}} - T_{\text{amb}})}{\text{Fuel Input} \times \text{GCV}} \times 100 $$

2.  **Loss due to moisture in fuel:** $$\displaystyle \frac{m_{\text{fuel}} \times \% \text{moisture} \times (h_{\text{fg}} + C_p \times (T_{\text{fg}} - T_{\text{amb}}))}{\text{Fuel Input} \times \text{GCV}} \times 100 $$

3.  **Loss due to moisture in air:** $$\displaystyle \frac{m_{\text{air}} \times \% \text{humidity} \times (h_{\text{fg}} + C_p \times (T_{\text{fg}} - T_{\text{amb}}))}{\text{Fuel Input} \times \text{GCV}} \times 100 $$

4.  **Loss due to unburnt carbon in ash/slag.**

5.  **Loss due to incomplete combustion (CO).**

6.  **Radiation & convection loss** (from boiler surface).

• GCV vs. NCV Basis Conversion:

  • GCV (Higher Heating Value): Includes latent heat of vaporization in products.

  • NCV (Lower Heating Value): Excludes latent heat (water remains vapor).

  • Conversion: $$\displaystyle \text{NCV} = \text{GCV} - 9 \times H \times \text{Latent Heat of Steam} $$

    where H = % hydrogen in fuel (by mass). Latent heat ≈ 2442 kJ/kg.

  • Efficiency on NCV basis: $$\displaystyle \eta_{\text{NCV}} = \eta_{\text{GCV}} \times \frac{\text{GCV}}{\text{NCV}} $$

Steam Distribution Systems (High Frequency)

• Objective: Deliver steam of required pressure & quality to users with minimum pressure drop & heat loss.

• Components: Steam header, distribution mains, branches, traps, drains, separators.

• Energy Conservation Measures:

  1. Proper Insulation: Minimize heat loss from pipes (use economic thickness).

  2. Drip Traps & Drain Points: Remove condensate at low points to prevent water hammer & heat loss.

  3. Pressure Reduction: Use PRVs close to user to avoid throttling.

  4. Minimize Leaks: Regular maintenance.

  5. Return Condensate: Recover heat & water.

  6. Separators & Strainers: Ensure dry steam for process.

Steam Traps (High Frequency)

• Working Principle: Automatic valve that discharges condensate, air, and non-condensable gases while preventing steam passage.

• Types (Brief):

  • Mechanical (Float & Thermostatic): Reliable, handles varying loads.

  • Thermostatic (Bimetallic, Bellows): Good for air venting, sensitive to superheat.

  • Thermodynamic (Disc): Simple, robust, but noisy, prone to wear.

• Performance Assessment Methods:

  1. Temperature Approach: Measure temp. at inlet & outlet. ΔT should be small (5-10°C for thermostatic, 0-5°C for float).

  2. Ultrasonic/Listening: Detect live steam blowing (hissing sound).

  3. Visual Inspection: (For open traps) See if condensate is discharging.

  4. Thermal Imaging: Cold trap = working; hot trap = failed open or blocked.

Furnace Concepts (High Frequency)

• Definition: An enclosed structure for generating heat (combustion or electrical) for industrial processes (heating, melting, drying).

• Classifications: By heat source (combustion, electric arc, induction), by operation (batch, continuous), by product (steel, glass, cement).

• Role in Steel Industry: Primary melting (BF, EAF), secondary refining (ladle furnace), reheating (soaking pit, walking beam furnace), heat treatment.

• Advantages of Minimum Excess Air:

  • Reduces heat loss in flue gas ($\propto$ excess air).

  • Reduces fuel consumption.

  • Reduces NOx formation (at high temps).

• How to Achieve:

  1. Optimize burner design (proper mixing, atomization).

  2. Use Oxygen Trim Control: Continuously measure O₂ in flue gas and adjust air flow.

  3. Regular maintenance of burners, dampers, and seals.

  4. Use high-quality combustion air (preheated, filtered).

Condensate Recovery and Flash Steam Utilization (High Frequency)

• Condensate Recovery: Returning hot condensate to boiler feedwater system.

  • Benefits: Saves fuel (pre-heats feedwater), saves water & treatment chemicals, reduces boiler blowdown.

• Flash Steam Utilization: When high-pressure condensate is throttled to a lower pressure, a portion flashes into steam (at lower pressure).

  • Process: High-pressure condensate → Flash vessel → Low-pressure flash steam (used in low-pressure process) + residual hot water.

  • Example: Condensate at 10 bar (180°C) discharged to 2 bar system. At 2 bar, saturation temp is 120°C. The enthalpy drop from 180°C to 120°C causes ~13% by mass of condensate to flash into steam at 2 bar.

  • Energy Saving: Captures latent heat otherwise lost in condensate.

Thermic Fluid Heating System

• Working: Closed-loop system. Thermic fluid (heat transfer oil) is heated in a coil-type heater (like a boiler without phase change) and circulated to heat exchangers in process. Fluid returns to heater.

• Preference over Steam:

  • No pressure → No boiler regulations, no blowdown, no steam traps.

  • Can achieve higher temperatures (300-400°C) at low pressure.

  • Precise temperature control.

  • No scaling/corrosion issues like in boilers.

  • Disadvantage: Fire risk (fluid degradation, leaks), higher initial cost.

E. ROTATING EQUIPMENT & HVAC

Centrifugal Pumps (High Frequency)

• Significance of Parallel Operation:

  • Increases flow rate to meet higher demand.

  • Provides redundancy (one can be serviced).

  • Improves part-load efficiency by running only required number of pumps.

• Factors Affecting Performance:

  • System Curve: Static head + friction head (∝ Flow²).

  • Pump Curve: Head vs. Flow (decreases with flow), Efficiency vs. Flow (bell-shaped), NPSH required.

  • Best Efficiency Point (BEP): Point of maximum efficiency on pump curve.

• Energy Conservation Opportunities:

  1. Avoid Throttling: Use variable speed drives (VSDs) instead of control valves.

  2. Right-Sizing: Select pump for BEP close to average system duty point.

  3. Series/Parallel Optimization: Use multiple smaller pumps instead of one large pump.

  4. Reduce System Resistance: Larger pipes, fewer bends, clean filters.

  5. Restore Wear: Replace worn impellers, clearances.

  6. Use High-Efficiency Motors.

Fans

• Design & Selection: Based on system curve (static pressure vs. flow). Select fan whose best efficiency point matches average duty point.

• Performance Evaluation: Measure flow, pressure, power input. Calculate Fan Laws for affinity:

$$ \frac{Q_1}{Q_2} = \frac{N_1}{N_2}, \quad \frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3, \quad \frac{\text{Power}_1}{\text{Power}_2} = \left(\frac{N_1}{N_2}\right)^3 $$

• Efficient Operation:

  • Use inlet guide vanes (IGVs) or VFDs for capacity control.

  • Ensure proper belt tension & alignment.

  • Minimize leakage (seals).

Refrigeration Plants

• Factors Affecting Performance & Energy Efficiency:

  1. Evaporator Temperature: Lower evaporator temp → higher compressor work.

  2. Condenser Temperature: Higher condenser temp → higher compressor work. Clean coils, cool condenser water.

  3. Compressor Type & Size: Screw/centrifugal more efficient than reciprocating at large capacity. Avoid over-sizing.

  4. Expansion Device: Thermostatic expansion valve (TXV) better than capillary.

  5. Suction & Discharge Pressure: High suction pressure (low superheat) & low discharge pressure (good subcooling) improve COP.

  6. Refrigerant Charge: Correct charge is critical.

  7. Heat Exchanger Effectiveness: Clean evaporator & condenser coils.

  8. Use VFDs on compressor motors for part-load.

F. FINANCIAL ANALYSIS & ECONOMICS (Very High Frequency)

Life Cycle Costing (LCC) (High Frequency)

• Definition: Total cost of owning and operating an asset over its entire life (from acquisition to disposal).

• Significance: Evaluates long-term cost-effectiveness, not just initial cost. Essential for comparing ECOs.

• Process:

  1. Identify all cost components: Initial Investment (I), Operating Costs (OC) (energy, maintenance), Replacement Costs, Salvage Value (S), Disposal Cost.

  2. Convert all future costs to Present Worth (PW) using discount rate i:

$$ \text{PW of Cost} = \text{Amount} \times (P/F, i\%, n) $$

3.  **LCC = I + Σ(PW of OC) - PW(S)**

• Applications: Equipment replacement, building design, project selection.

• Effect: Favors options with higher initial cost but lower operating cost (e.g., premium efficiency motors).

Payback Period (High Frequency)

• Simple Payback Period (SPP): Time required for cumulative savings to equal initial investment.

$$ \text{SPP (years)} = \frac{\text{Initial Investment (Rs)}}{\text{Annual Net Savings (Rs/year)}} $$

• Significance of Risk Analysis: Longer payback implies higher risk (uncertainty in future savings, technology obsolescence, company stability). Shorter payback preferred for risky projects.

• Merits: Simple, easy to understand, emphasizes liquidity.

• Demerits: Ignores cash flows beyond payback, ignores time value of money, ignores risk explicitly.

Net Present Value (NPV) (High Frequency)

• Concept: Sum of all future cash inflows & outflows (savings & costs) discounted to present value.

$$ \text{NPV} = -I_0 + \sum_{t=1}^{n} \frac{S_t}{(1+i)^t} - \sum_{t=1}^{n} \frac{C_t}{(1+i)^t} + \frac{S_n}{(1+i)^n} $$

where `I₀` = initial investment, `Sₜ` = annual savings, `Cₜ` = annual costs (excluding depreciation), `Sₙ` = salvage value, `i` = discount rate, `n` = life.

• Decision Rule: Accept if NPV > 0 (project earns more than discount rate).

• Advantages over SPP:

  • Considers time value of money.

  • Considers entire life of project.

  • Directly measures wealth creation.

  • Can incorporate risk via risk-adjusted discount rate.

• Discount Rate: Minimum attractive rate of return (MARR), cost of capital, hurdle rate.

• Discount Period: Life of the project or analysis period.

Internal Rate of Return (IRR)

• Definition: Discount rate at which NPV = 0. It is the break-even rate of return.

• Calculation: Trial & error or using financial calculator/Excel (=IRR(values)).

• Decision Rule: Accept if IRR > Discount Rate (MARR).

• Comparison with NPV: Both consider time value. NPV is absolute (Rs), IRR is relative (%). NPV is generally preferred for mutually exclusive projects due to reinvestment rate assumption.

ESCO (Energy Service Company) Concept (High Frequency)

• Basic Concept: A company that provides comprehensive energy solutions to clients. The key feature is Performance Contracting.

• Business Model:

  1. ESCO conducts free/paid energy audit.

  2. Proposes ECOs with guaranteed savings.

  3. Finances the project (often 100%).

  4. Implements & verifies savings.

  5. Recovers investment from the client's actual energy savings (shared savings or guaranteed savings model).

  6. After payback, savings accrue to client.

• Advantages for Client: No upfront cost, technical expertise, guaranteed savings, off-balance sheet financing.

• Risk: ESCO bears performance risk.

G. LIGHTING SYSTEMS (High Frequency)

Scope of Energy Conservation in Lighting

• Replace inefficient lamps: Incandescent → CFL → LED.

• Optimize lighting levels: Use only required lux (task lighting).

• Improve maintenance: Clean fixtures, replace aging lamps.

• Use efficient controls: Occupancy sensors, daylight harvesting, timers, dimmers.

• Right-sizing fixtures: Avoid over-lighting.

• Use efficient ballasts: Electronic vs. magnetic.

• Optimize layout & spacing.

LED Lighting

• Advantages over Conventional:

  • High Efficacy: 100-150 lm/W vs. 60-100 for CFL, 15 for incandescent.

  • Long Life: 50,000-100,000 hrs.

  • Instant On, No UV/IR.

  • Directional light (no reflector losses).

  • Dimmable, color tunable.

  • Rugged, no filament.

• Considerations: Higher initial cost, quality variation (driver, thermal management), color rendering index (CRI), color temperature (CCT).

Lamp Replacement Strategy Calculation (Numerical)

• Given: Old lamp (W_old, life L_old, cost C_old), New lamp (W_new, life L_new, cost C_new), Operating hours (H), Electricity cost (Rs/kWh).

• Steps:

  1. Annual Energy Consumption:

     $$\displaystyle E_{\text{old}} = \frac{W_{\text{old}} \times H}{1000} $$ kWh; $$\displaystyle E_{\text{new}} = \frac{W_{\text{new}} \times H}{1000} $$ kWh.

  2. Annual Energy Savings: $$\displaystyle \Delta E = E_{\text{old}} - E_{\text{new}} $$ kWh.

  3. Annual Cost Savings: $$\displaystyle \Delta C_{\text{energy}} = \Delta E \times \text{Rate} $$.

  4. Annual Lamp Replacement Cost:

     Number of lamps needed/year = $$\displaystyle \frac{H}{L} $$.

     $$\displaystyle C_{\text{rep,old}} = \frac{H}{L_{\text{old}}} \times C_{\text{old}} $$; similarly for new.

     $$\displaystyle \Delta C_{\text{rep}} = C_{\text{rep,old}} - C_{\text{rep,new}} $$.

  5. Total Annual Net Savings: $$\displaystyle \Delta S = \Delta C_{\text{energy}} + \Delta C_{\text{rep}} $$.

  6. Simple Payback Period: $$\displaystyle \text{SPP} = \frac{C_{\text{new}} - C_{\text{old}}}{\Delta S} $$ years.

  7. Note: If lamp life differs, consider replacement cost stream in LCC/NPV for accuracy.

Illumination (Lux)

• Definition: SI unit of illuminance. 1 Lux = 1 lumen/m².

• Luminous Flux (Lumen, lm): Total light output from source.

• Luminous Intensity (Candela, cd): Light emitted in a direction (lm/sr).

• Illuminance (E) on a Surface: $$\displaystyle E = \frac{\Phi}{A} $$ (for uniform flux).

• Inverse Square Law: $$\displaystyle E \propto \frac{1}{d^2} $$ (for point source).

• Cosine Law: $$\displaystyle E = \frac{I \cos\theta}{d^2} $$ (for tilted surface).

• Recommended Lux Levels (IS/CIE): Office (300-500 lux), Industry (150-300 lux), Street (20-30 lux).

Procedure to Save Energy in Lighting Systems

1. Audit: Measure existing illuminance (Lux meter), count lamps, note types & hours.

2. Set Standards: Compare with recommended lux levels (IS/CIE).

3. Identify Measures: Relamping to LED, de-lamping, using sensors, optimizing layout.

4. Calculate Savings: For each measure (use lamp replacement method).

5. Prioritize: Based on payback/NPV.

6. Implement & Verify: Post-installation lux measurement.

H. CASE STUDIES & PROBLEM-SOLVING

Boiler Load Optimization Problem

• Given: Multiple identical/different boilers with part-load efficiency curves.

• Principle: Total steam demand may be met by different combinations. Total fuel consumption = Σ (Steam output / Efficiency) for each boiler.

• Steps:

  1. For each boiler, calculate fuel required at various loads (e.g., 25%, 50%, 75%, 100%).

  2. For total demand (e.g., 20 TPH), list all feasible combinations (e.g., 2 boilers @ 10 TPH each, or 1 @ 15 TPH + 1 @ 5 TPH).

  3. Calculate total fuel consumption for each combination.

  4. Select combination with MINIMUM total fuel consumption.

  5. % Savings = $$\displaystyle \frac{\text{Fuel}_{\text{base}} - \text{Fuel}_{\text{opt}}}{\text{Fuel}_{\text{base}}} \times 100\% $$

• Key Insight: Efficiency often drops at very low loads (<30%). Running one boiler at high load & another at very low load may be worse than running both at medium load.

Integrated PF Correction & Penalty Avoidance Problem

• Combines PF calculation and penalty avoidance.

• Steps:

  1. Calculate existing kW from given kVA & PF.

  2. Determine kVAr needed to reach minimum PF (avoid penalty).

  3. Check if proposed capacitor (e.g., 100 kVAr) is sufficient. If not, calculate required kVAr.

  4. Calculate new kVA after installing capacitor (using kW & new kVAr).

  5. Calculate improved PF.

  6. If improved PF ≥ min PF → No penalty. Else, calculate penalty based on % dip.

Motor Loading Determination from Input Parameters

• Given: V, I, PF, η_FL, P_rated.

• Approximation (if load > 75%): Assume η_actual ≈ η_FL.

  • P_out (kW) = √3 × V × I × PF × η_FL / 1000.

  • % Loading = (P_out / P_rated) × 100.

• For accurate result at low load: Use motor part-load efficiency curve (from manufacturer/data book). Find η at calculated kW output, iterate if needed.

Financial Evaluation Problem (NPV/LCC for Lighting Retrofit)

• Given: Initial cost, annual energy savings, lamp life, discount rate, analysis period.

• Steps for NPV:

  1. Annual Net Savings (S): Savings in energy + maintenance - cost of new lamp replacements (if any).

  2. For each year t (1 to n), calculate Present Worth (PW) of savings: $$\displaystyle PW_t = \frac{S}{(1+i)^t} $$

  3. PW of Initial Cost: = -I₀ (at t=0).

  4. NPV = -I₀ + Σ PW_t.

  5. Decision: NPV > 0 → Accept.

• LCC Approach: Compare LCC of existing system vs. new system over analysis period. Choose lower LCC.

Exam Tips & Common Pitfalls:

• PF Problems: Always calculate kW first. Remember: $$\displaystyle \text{kW} = \text{kVA} \times \text{PF} $$. New PF = $$\displaystyle \cos[\tan^{-1}((\text{kVAr}_{\text{old}}-\text{kVAr}_{\text{cap}})/\text{kW})] $$.

• Boiler Efficiency: Distinguish clearly between Direct (output/input) and Indirect (100 - losses). For GCV/NCV, remember NCV < GCV, so efficiency on NCV basis will be higher numerically.

• NPV vs. Payback: NPV is superior. Always show formula and discounting steps. For SPP, note it ignores time value.

• Motor Loading: Do not use input power directly as output. Multiply by efficiency.

• Steam Traps: Know the temperature approach method for assessment.

• ESCO: Emphasize Performance Contracting and No-Upfront-Cost for client.

• Diagrams: Be prepared to sketch: Steam trap (float type), furnace zones, pump system curve vs. pump curve, simple ESCO model.