Power Cable Resistance for Direct Current...•Sheath current losses (for cables with sheaths) –OR, obtain ac resistance from appropriate tables: •Westinghouse T & D Reference

Traction Power Load Flow Simulation

Electrical Conductor Modeling

• Power Cable Resistance for Direct Current

– Cable resistance changes with conductor temperature

– What conductor temperature to use? Cable rated maximum operating temperature is worst-case, and often used

Use cable ampacity program to obtain more precision

– Obtain dc resistance at reference temp. (R20 ) from tables (Std. Handbook for Electrical Engineers is excellent resource)

– Temp. adjust. to 90 Deg. C: R90 = R20 [1 + α(t90-t20) ] α = 0.00393 for soft-drawn copper (at 20 Deg. C ref. temp)

Values for α for other materials are in Standard Handbook

Example: R90 = R20 [1 + α(t90-t20) ] = [1 + 0.00393(90-20)]

= 1.275 x R201

R. W. Benjamin Stell

Traction Power Load Flow SimulationElectrical Conductor Modeling

• Power Cable Resistance for Alternating Current

– Obtain dc resistance from tables and adjust for:

• Temperature (same as approach used for dc cables)

• Skin effect (increases significantly with cable diameter)

• Proximity effect (should be negligible with proper design)

• Sheath current losses (for cables with sheaths)

– OR, obtain ac resistance from appropriate tables:

• Westinghouse T & D Reference Book Chapter 3, Characteristics of Aerial Lines (Ω/mile for 0, 25, 50, and 60 Hz)

• Westinghouse T & D Reference Book Chapter 6, Electrical Characteristics of Cables

2R. W. Benjamin Stell


• Power Cable Reactance (Inductance and Capacitance)

– Obtain reactance from tables…carefully!

• Single phase circuits for traction power

• Reactance and capacitance at one foot spacing (xa and xa’)

• Adjust for actual conductor spacing (xd)

• 25, 50 and 60 Hz values provided in Westinghouse T&D Book

– OR, calculate based on inductance & capacitance formulas for single phase circuits (recommended)

– Assumptions used need to match those of the simulation program being used (loop versus partial values, for example)



• Contact Wire Resistance Calculations

– New wire: obtain dc resistance from contact wire manufacturer tables and adjust for operating temperature

α20 for hard-drawn copper is 0.00383 per deg. C (ASTM B47)

α20 for bronze alloy is 0.00314 per Deg. C (ASTM B9)

– Worn wire: 30% wear is typical (worst-case) assumption

– Example for 30% wire wear (70% remaining section)

Wire resistance: R = volume resistivity x [length/area] = ρL/A Ω

30% worn wire: RWORN = ρL/[0.7 x A] = 1.429 x RNEW

– Resource: June 1992 APTA Rapid Transit Conference Paper, “Direct Current Coordination for Electrified Transit”, B. Stell



• Contact Wire Maximum Operating Temperatures (“Continuous” Temperatures)– Electrolytic hard drawn copper (alloy C11000): 75 Deg. C

– Silver bearing copper (alloy C10700): 100 Deg. C

– Bronze alloy 80 (alloy C16200): 100 Deg. C

– Annealing of wire (cumulative weakening) can occur at temperatures significantly above these

– How much higher? For more information: See June 1994 APTA Rapid Transit Conference paper, “Protection of Trolley & Messenger Wire from Thermal Damage Due to Short Circuits”, by B. Stell

– Ask the manufacturers!

– Op. temp. may also be limited by OCS design (sag/tension)5R. W. Benjamin Stell



• Running Rail Resistance (Direct Current)

– Difficult to obtain resistance data from rail manufacturers

– Chemical composition and tempering affect rail resistance

– Resistances can be found in older Elect. Engineer’s Handbooks

– Or, calculate from volume resistivity: Resistance = ρL/A

– Rail operating temp.: 70 Deg. C is realistic maximum for CWR

– 10% railhead wear is typical assumption for resistance calcs

– See June 1992 APTA Rapid Transit Conference Paper, “Direct Current Coordination for Electrified Transit”, for more information/data



• Steel Contact Rail Resistance (150 lb RE, typical)

– Low resistance steel alloy (≈ 3.5 to 3.8 mΩ/1000)

– Resistance varies significantly with chemical composition

• Composite and Aluminum Contact Rail Resistances

– 84C, 85C composite sections standard in USA (2.0 mΩ/1000 ft.)

– All aluminum rail: available to 1.2 mΩ/1000 ft. (TransTech 7L)



Rail Resistance Data from 1992 APTA Paper




• OCS Conductor Reactance (XL = jωL)

– Calculate circuit inductance using method of flux linkages

– Good textbook: Elements of Power Systems Analysis by W. D. Stevenson (also Electric Power Transmission by L.F. Woodruff)

– Need distances of all parallel conductors to each other (ROW section view with X-Y coordinates for circuits is helpful)

– Need geometric mean radius (GMR) of each conductor

– Calculate GMR for groups of phase and return conductors

– Calculate geometric mean distance (GMD) between phase and return conductor groups

– See APTA 1992 paper for application examples

– Some load flow programs will calculate circuit reactance


Load Flow Simulation - Electrical Conductor Modeling

OCS Circuit Inductance Calculations

Application Example from 1992 APTA Paper (see paper for explanations of variables)

Single OCS Circuit with Two Tracks (Four Rails)

Find geometric mean distances between phase and return conductor groups to calculate inductance using two wire formula



• Impedance of Steel Running Rails (Alternating Current)

– Steel rails are highly inductive (exhibit significant skin effect and hysteresis)

– Self inductance decreases, and resistance increases, with increasing frequency

– Impedance increases with current flowing in the rail (nonlinear)

– See Paper: “Determination of Rail Internal Impedance for Electric Railway Traction System Simulation”, R. J., Hill & D. C. Carpenter, IEE Proceedings 1991

– Also: “Resistance and Internal Inductance of Traction Rails at Power Frequency: A Survey”, A. Mariscotti and P. Pozzobon, IEEE Transactions on Vehicular Technology, July 2004



12

Mariscotti and Pozzobon, 2004

Figures Show Variation of Rail Resistance and Internal Inductance with Rail Current

Modeling: Use highest expected value of rail impedance ORadjust impedance iteratively to match rail current

R. W. Benjamin Stell

Documents

Power Cable Resistance for Direct Current...•Sheath current losses (for cables with sheaths) –OR, obtain ac resistance from appropriate tables: •Westinghouse T & D Reference