PE Exam Exam > PE Exam Notes > Electrical & Computer Engineering for PE > Cheatsheet: Distribution
Cheatsheet: Distribution
1. Distribution System Basics
1.1 Voltage Levels
| System Type | Voltage Range |
|---|---|
| Primary Distribution | 4.16 kV to 34.5 kV (common: 12.47 kV, 13.8 kV, 22.9 kV, 34.5 kV) |
| Secondary Distribution | 120/240 V (single-phase), 208Y/120 V, 480Y/277 V (three-phase) |
| Utilization | 120 V, 240 V, 480 V, 600 V |
1.2 System Configurations
| Configuration | Characteristics |
|---|---|
| Radial | Single path from source to load; lowest cost; least reliable |
| Loop (Open Ring) | Normally open loop; manual or automatic switching; improved reliability |
| Network | Multiple sources; highest reliability; highest cost; used in high-density urban areas |
| Primary Selective | Two sources with manual/automatic transfer; improved continuity |
2. Distribution Transformers
2.1 Transformer Connections
| Connection | Application |
|---|---|
| Delta-Wye (Δ-Y) | Most common; primary delta, secondary wye; provides neutral for single-phase loads |
| Wye-Delta (Y-Δ) | Secondary delta for three-phase loads without neutral |
| Delta-Delta (Δ-Δ) | Open delta capability; can operate with one transformer failed at 58% capacity |
| Wye-Wye (Y-Y) | Requires grounded neutral or tertiary winding to prevent overvoltage |
2.2 Transformer Ratings and Sizing
- kVA rating = √3 × VL-L × IL (three-phase)
- kVA rating = V × I (single-phase)
- Standard distribution transformer ratings: 10, 15, 25, 37.5, 50, 75, 100, 167, 250, 333, 500 kVA
- Impedance: 1.5% to 5.75% for distribution transformers
- Load factor affects sizing; diversity factor = 1.0 to 2.5 for residential
2.3 Transformer Losses and Efficiency
| Parameter | Formula/Value |
|---|---|
| Core Loss (No-load) | Constant; independent of load; 0.1% to 0.3% of rating |
| Copper Loss (Load) | I²R losses; varies with load squared; 1% to 2% at full load |
| Efficiency | η = Pout / (Pout + Pcore + Pcopper) |
| All-day Efficiency | ηall-day = (kWh output in 24h) / (kWh input in 24h) |
3. Voltage Regulation
3.1 Voltage Drop Calculations
| Formula | Application |
|---|---|
| VD = I(R cosθ + X sinθ) | Per-phase voltage drop (line-to-neutral) |
| %VD = (VD / Vnom) × 100 | Percent voltage drop |
| VD3φ = √3 × I × Z | Line-to-line voltage drop (approximate) |
| VD = (2 × I × L × R) / 1000 | Single-phase, two-wire (VD in volts, L in feet, R in Ω/1000 ft) |
3.2 Voltage Regulation Limits
- ANSI C84.1 Range A: ±5% of nominal (preferred)
- ANSI C84.1 Range B: +5.8%/-8.3% (tolerable)
- Maximum feeder drop: 3% recommended
- Maximum branch circuit drop: 3% recommended
- Total drop (feeder + branch): 5% maximum
3.3 Voltage Regulation Equipment
| Device | Description |
|---|---|
| LTC (Load Tap Changer) | Substation transformer tap changer; ±10% in 32 steps (0.625% per step); automatic operation |
| Step Voltage Regulator | ±10% in 32 steps; single-phase or three-phase; line-drop compensation |
| Switched Capacitor Banks | Reactive power compensation; improves voltage and power factor |
3.4 Line-Drop Compensation
- R and X settings compensate for feeder impedance
- Maintains voltage at a point beyond regulator location
- R setting (volts) = Iload × Rline × CT ratio / PT ratio
- X setting (volts) = Iload × Xline × CT ratio / PT ratio
4. Power Factor and Reactive Power
4.1 Power Factor Fundamentals
| Parameter | Formula |
|---|---|
| Power Factor | PF = P / S = cos θ = kW / kVA |
| Apparent Power | S = √(P² + Q²) or S = V × I (kVA) |
| Reactive Power | Q = S × sin θ = P × tan θ (kVAR) |
| Real Power | P = S × cos θ = V × I × cos θ (kW) |
4.2 Capacitor Sizing
| Formula | Description |
|---|---|
| Qcap = P(tan θ1 - tan θ2) | Required kVAR to improve PF from θ1 to θ2 |
| Qcap = V² / XC | Capacitor reactive power |
| XC = 1 / (2πfC) | Capacitive reactance |
| Icap = Qcap / (√3 × VL-L) | Three-phase capacitor current |
4.3 Capacitor Bank Ratings
- Standard three-phase ratings: 300, 450, 600, 900, 1200, 1800 kVAR
- Voltage ratings: 2.4, 4.16, 4.8, 7.2, 12.47, 13.8, 14.4, 24.94, 34.5 kV
- Grounded wye most common for distribution
- Switched capacitors: 2-4 steps for voltage and VAR control
4.4 Benefits of Power Factor Correction
- Reduced line losses: Loss reduction = 1 - (PFold/PFnew)²
- Increased system capacity: released kVA = kW × (1/PFold - 1/PFnew)
- Improved voltage regulation: reduces voltage drop
- Reduced demand charges (utility billing)
5. Conductor Selection and Sizing
5.1 Conductor Ampacity
- Based on: conductor material, insulation type, ambient temperature, number of conductors
- Ampacity adjustment: multiply table values by correction factors
- Temperature correction factor: 0.82 at 40°C, 0.91 at 30°C (75°C insulation)
- Conductor bundling derating: 0.80 for 4-6 conductors, 0.70 for 7-9 conductors
5.2 Conductor Properties
| Property | Aluminum |
|---|---|
| Resistivity (DC at 20°C) | 2.83 × 10⁻⁸ Ω·m (Cu: 1.72 × 10⁻⁸ Ω·m) |
| Weight | 30% of copper weight for same ampacity |
| Cost | Lower than copper per unit length |
| Common Types | ACSR, AAC, AAAC (aluminum); Cu, THHN/THWN (copper) |
5.3 Economic Conductor Size
- Kelvin's Law: economical size when annual cost of losses equals annual fixed charges on conductor investment
- Total cost = installed cost + present worth of losses over lifetime
- Loss cost = 3 × I² × R × hours × $/kWh × demand factor²
5.4 Voltage Drop Limits for Conductor Sizing
- Primary feeders: 3% maximum at peak load
- Secondary feeders: 2% maximum
- Service drops: 1% maximum
- Combined primary and secondary: 5% total maximum
6. Protective Devices
6.1 Overcurrent Protection Devices
| Device | Characteristics |
|---|---|
| Fuses | Single operation; K, T, N types; coordination by time-current curves; economical |
| Reclosers | Automatic interruption and reclosing; 1-4 operations; oil or vacuum; 560-1120 A |
| Sectionalizers | Counts fault current; opens after backup device operates; 3 counts standard |
| Circuit Breakers | Manual/automatic operation; adjustable settings; reusable; higher cost |
6.2 Fuse Ratings and Types
| Fuse Type | Speed/Application |
|---|---|
| K (Fast) | 6-8 times rating melting time; lateral and transformer protection |
| T (Slow) | 10-13 times rating melting time; feeder protection; cold-load pickup |
| N (Slow) | Similar to T; improved coordination |
- Standard current ratings: 6, 10, 15, 25, 40, 65, 100, 140, 200 A
- Voltage ratings: 2.4, 4.8, 7.2, 14.4, 23.0, 34.5, 46, 69 kV
6.3 Coordination Principles
- Time-current curve separation: minimum 0.2-0.3 seconds at all current levels
- Fuse-to-fuse: downstream fuse total clear time < upstream="" fuse="" minimum="" melt="">
- Recloser-to-fuse: fuse saves on temporary faults; recloser fast curve < fuse="" melt;="" recloser="" slow="" curve=""> fuse clear
- Instantaneous trip must not operate for downstream fault maximum
6.4 Recloser Operations
- Sequence: 2 fast operations, 2 slow operations (common)
- Fast operation: 0.1-0.3 seconds
- Slow operation: 1-10 seconds
- Reclosing intervals: 1-2 seconds (first), 10-30 seconds (subsequent)
- 85% of faults are temporary; cleared by fast reclosing
7. Short Circuit Analysis
7.1 Fault Current Calculations
| Formula | Application |
|---|---|
| Isc = V / Ztotal | Basic fault current (per-phase) |
| Isc-3φ = VL-L / (√3 × Z1) | Three-phase fault current |
| Isc-SLG = 3VL-N / (Z1 + Z2 + Z0) | Single line-to-ground fault |
| Isc-LL = √3 × VL-N / (Z1 + Z2) | Line-to-line fault |
7.2 Impedance Values
| Component | Typical Impedance |
|---|---|
| Utility Source | Z = V² / MVAsc; X/R = 10-20 |
| Transformer | Z = %Z × V² / (100 × kVA); X/R = 3-7 |
| Cable (per 1000 ft) | R: 0.05-2 Ω; X: 0.02-0.08 Ω |
| Overhead Line | R: 0.1-1.5 Ω/mile; X: 0.6-1.2 Ω/mile |
7.3 Per-Unit Method
| Parameter | Formula |
|---|---|
| Base kVA | Choose system base (e.g., 10 MVA or 100 MVA) |
| Base Voltage | System line-to-line voltage |
| Base Current | Ibase = kVAbase / (√3 × kVbase) |
| Base Impedance | Zbase = kVbase² / MVAbase |
| Per-Unit Impedance | Zpu = Zactual / Zbase |
| Change Base | Zpu-new = Zpu-old × (kVAnew/kVAold) × (kVold/kVnew)² |
7.4 Symmetrical Components
- Positive sequence (Z1): normal balanced system impedance
- Negative sequence (Z2): typically Z2 ≈ Z1 for static equipment
- Zero sequence (Z0): ground return path; Z0 = 2-5 × Z1 for overhead lines
- Used for unbalanced fault analysis
8. Grounding Systems
8.1 System Grounding Types
| Grounding Type | Characteristics |
|---|---|
| Solidly Grounded | Neutral directly grounded; Z0/Z1 < 3;="" high="" fault="" current;="" most="" common="" in=""> |
| Resistance Grounded | Limits ground fault current; reduces transient overvoltages; 200-400 A limit common |
| Reactance Grounded | Limits fault current but higher than resistance; reduces arcing ground damage |
| Ungrounded | No intentional ground; high transient overvoltages; not used in modern distribution |
8.2 Equipment Grounding
- Grounding electrode conductor sizing: based on largest service conductor (NEC Table 250.66)
- Grounding electrode resistance: 25 Ω maximum (NEC), 5 Ω preferred
- Ground rod: 5/8 inch diameter, 8 ft minimum length (copper-clad steel)
- Two rods required if single rod exceeds 25 Ω; spacing ≥ 6 ft
8.3 Ground Fault Protection
- Ground fault relaying: residual connection (3I0) or zero-sequence CT
- Pickup setting: 20-40% of maximum three-phase fault current at end of zone
- Time delay: 0.1-0.5 seconds coordination margin
- Sensitive ground fault: 5-50 A pickup for high-resistance faults
8.4 Touch and Step Potential
| Parameter | Formula/Value |
|---|---|
| Touch Potential Limit | Vtouch = (1000 + 1.5ρs) / √ts |
| Step Potential Limit | Vstep = (1000 + 6ρs) / √ts |
- ρs = surface layer resistivity (Ω·m); ts = shock duration (sec)
- Crushed rock (3000 Ω·m) reduces shock hazard
9. Load Characteristics
9.1 Load Types and Power Factors
| Load Type | Power Factor |
|---|---|
| Incandescent Lighting | 1.0 (unity) |
| Fluorescent Lighting | 0.85-0.95 lagging (with ballast) |
| Induction Motors | 0.75-0.85 lagging (full load); 0.2-0.5 (no load) |
| Resistance Heating | 1.0 (unity) |
| Power Supplies/Electronics | 0.6-0.9 (varies with harmonic content) |
9.2 Demand and Diversity
| Term | Definition |
|---|---|
| Demand | Average load over specified time interval (15-30 min) |
| Maximum Demand | Highest demand during specified period |
| Demand Factor | DF = Maximum Demand / Connected Load |
| Diversity Factor | Div = Sum of Individual Max Demands / Coincident Max Demand |
| Load Factor | LF = Average Load / Peak Load (over period) |
| Utilization Factor | UF = Maximum Demand / Rated Capacity |
9.3 Typical Demand Factors
- Residential: 0.4-0.6 (first 10 kW at 100%, remainder at 40%)
- Commercial: 0.75-0.85
- Industrial: 0.8-0.9
- Diversity factor residential feeders: 1.5-2.5
9.4 Load Growth and Forecasting
- Annual growth rates: residential 2-4%, commercial 3-5%, industrial varies
- Planning horizon: 5-10 years for distribution
- Load density: urban 1500-5000 kVA/sq mi, suburban 500-1500 kVA/sq mi
10. Reliability and Power Quality
10.1 Reliability Indices
| Index | Formula |
|---|---|
| SAIFI | System Average Interruption Frequency Index = Total Customer Interruptions / Total Customers |
| SAIDI | System Average Interruption Duration Index = Sum Customer Interruption Durations / Total Customers (min) |
| CAIDI | Customer Average Interruption Duration Index = SAIDI / SAIFI (min) |
| ASAI | Average Service Availability Index = (Total Hours - Outage Hours) / Total Hours |
10.2 Power Quality Disturbances
| Disturbance | Characteristics |
|---|---|
| Sag (Dip) | 0.1-0.9 pu voltage; 0.5 cycle to 1 min duration; motor starting, faults |
| Swell | 1.1-1.8 pu voltage; short duration; load rejection, single-phase fault |
| Interruption | < 0.1="" pu="" voltage;="" momentary="">< 3="" sec),="" temporary="" (3="" sec="" -="" 1="" min),="" sustained="" (=""> 1 min) |
| Transient | High magnitude, short duration; lightning, switching; 0.3-50 μs |
| Flicker | Voltage variation 0.95-1.05 pu; < 25="" hz="" modulation;="" arc=""> |
10.3 Harmonics
| Parameter | Formula/Limit |
|---|---|
| THD (Voltage) | THDV = √(V2² + V3² + ... + Vn²) / V1 × 100% |
| THD (Current) | THDI = √(I2² + I3² + ... + In²) / I1 × 100% |
| IEEE 519 Voltage Limit | THD < 5%="" at="" pcc="" (individual="" harmonic=""><> |
| IEEE 519 Current Limit | Depends on Isc/IL ratio; THD 5-20% |
- Triplen harmonics (3rd, 9th, 15th): add in neutral; can exceed phase current
- 5th and 7th harmonics: dominant in six-pulse converters
- Harmonic filters: series or parallel tuned to specific harmonics
10.4 Voltage Unbalance
| Parameter | Formula |
|---|---|
| Voltage Unbalance | VU% = (Max deviation from avg) / Vavg × 100 |
| NEMA Limit | 1% maximum for motors (derate 2% per 1% VU beyond) |
- Causes: unbalanced loads, single-phase laterals, open phases
- Effects: motor overheating, negative-sequence currents, reduced life
11. Distribution Automation
11.1 Automated Switching Devices
| Device | Function |
|---|---|
| Automated Recloser | SCADA-controlled; remote operation; fault location; 1-3 cycles |
| Automated Switch | Remote-controlled sectionalizing; no fault interruption; service restoration |
| Fault Interrupter | Automated protection device; 600-800 A rating |
11.2 SCADA Functions
- Supervisory Control and Data Acquisition
- Real-time monitoring: voltage, current, power, status
- Remote control: switch operations, tap changing, capacitor switching
- Alarm management and event logging
- Data acquisition interval: 2-10 seconds
11.3 Fault Location Identification
- Impedance-based: Z = V/I; distance = Z × line length / Ztotal
- Traveling wave: location from time-of-arrival difference; accuracy ±200 m
- Fault indicators: visual/remote indication of fault passage
- Smart meters: voltage sag detection and reporting
11.4 Advanced Distribution Management
- Volt-VAR Optimization (VVO): minimize losses while maintaining voltage limits
- Fault Location, Isolation, Service Restoration (FLISR): automatic switching to restore service
- Conservation Voltage Reduction (CVR): reduce voltage to reduce consumption; CVR factor 0.5-1.0
- Distribution Management System (DMS): advanced analytics and control
12. Underground Distribution
12.1 Cable Types
| Type | Application |
|---|---|
| XLPE (Cross-linked Polyethylene) | Most common; 90°C rating; primary and secondary |
| EPR (Ethylene Propylene Rubber) | High flexibility; 90-105°C rating; wet/dry locations |
| PILC (Paper Insulated Lead Covered) | Older installations; being replaced; 85°C rating |
| Concentric Neutral | Primary cable; neutral wires helically wrapped |
| Tape Shield | Primary cable; copper tape neutral; single-point grounded |
12.2 Cable Ampacity Derating
- Soil thermal resistivity: 90 °C·cm/W standard; derate for higher values
- Burial depth derating: 0.97 at 36 inches, 0.94 at 48 inches
- Multiple cables: 0.80 for 2 cables, 0.70 for 3 cables, 0.65 for 4 cables (in same trench)
- Load factor: cable can be oversized based on cyclic loading
12.3 Cable Impedance
- RAC > RDC due to skin effect and proximity effect
- Skin effect factor: 1.0 at 60 Hz for small conductors, up to 1.05 for large
- Geometric mean radius (GMR) used for reactance calculations
- Sheath/shield bonding affects impedance and losses
12.4 Underground System Configurations
| Configuration | Description |
|---|---|
| Radial | Single feed; pad-mounted transformers; lowest cost |
| Loop | Open loop with sectionalizing switches; improved reliability |
| Primary Network | Grid of primary feeders; highest reliability; highest cost |
| Secondary Network | Low-voltage grid; multiple sources; urban high-density areas; 216Y/125 V or 480Y/277 V |
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