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Line Calculations

Line is a core calculation object. It combines a LineDesign and a Conductor and exposes all technical analysis methods.

Construction

from refa import Line, LineDesign
from refa.defaults import default_clear_environment, acss_795_0_cuckoo

ld = LineDesign(
    environment=default_clear_environment(),
    nbr_circuits=1, nbr_bundles=3, nbr_conds_per_bundle=1,
    length_km=10, avg_span_m=250, max_span_m=300,
)

line = Line(line_design=ld, conductor=acss_795_0_cuckoo())
# or: line = ld + acss_795_0_cuckoo()

Thermal Calculations (IEEE 738)

REFA implements the IEEE 738 steady-state thermal balance to calculate conductor temperature, resistance, and ampacity.

Ampacity

Maximum current the conductor can carry without exceeding its maximum (rated) temperature at the given environmental conditions. Updating the maximum temperature of the conductor will result in a different current rating (ampacity).

ampacity = line.ampacity_at_environment()
# 1398 A

Conductor Temperature

Given the peak current in the line, the conductor temperature can be calculated using IEEE 738. 

# From current
temp = line.temperature_at_current(current_a=1400)           # 200 °C
temp = line.temperature_at_current(power_mw=550, voltage_kv=345)  # 106 °C

Conductor Resistance

Resistance interpolated between the low and high temperature reference points.

res = line.resistance_at_current(current_a=1400)             # Ω/m
res = line.resistance_at_current(power_mw=550, voltage_kv=345)

Current vs. power+voltage

Most Line methods accept either current_a or the pair (power_mw, voltage_kv), but not both. REFA deduced current from power and voltage to current using:

  • AC (3-phase): I = P / (√3 · V)
  • DC: I = P / (nbr_poles · V)

Sag Calculations (CIGRÉ 324)

REFA implements the CIGRÉ 324 catenary sag-tension model. All sag methods require an initial_tension_percentage — the initial stringing tension as a fraction of the conductor's rated tensile strength (RTS).

Sag at Steady-State Current

sag = line.sag_at_current(
    current_a=1400,
    initial_tension_percentage=0.2,   # 20% of RTS
)
# 13.6 m

Sag at Power and Voltage

sag = line.sag_at_power_and_voltage(
    power_mw=500, voltage_kv=230,
    initial_tension_percentage=0.2,
)

Sag at a Known Conductor Temperature

sag = line.sag_at_temperature(
    temp_at_current_c=85,
    initial_tension_percentage=0.2,
)
# 10.8 m

Sag Under Mechanical Loading (NESC 250B)

from refa.standards import nesc_250b_heavy

sag = line.sag_at_loading(
    loading_conditions=nesc_250b_heavy(),
    initial_tension_percentage=0.2,
)
# 11.6 m — includes wind pressure and ice load

Corona (AC and DC)

Corona calculations require a StructureConfig to define phase spacing and structure geometry.

from refa.defaults import default_structure_config_ac, default_structure_config_dc

config_ac = default_structure_config_ac()

# Inception voltage — voltage at which corona begins
v_inc = line.corona_inception_voltage(structure_config=config_ac)   # 230 kV

# Voltage gradient at the conductor surface
v_grad = line.corona_voltage_gradient(structure_config=config_ac)   # 29 kV/cm

For DC lines, pass is_hvdc=True and a StructureConfigDC:

config_dc = default_structure_config_dc()
v_inc_dc = line.corona_inception_voltage(structure_config=config_dc, is_hvdc=True)

Losses

Resistive Losses

Annual line losses in MWh/m per year, accounting for a load factor.

The utilization factor of the line is computed as: UF = 0.3 × load_factor + 0.7 × load_factor²

# From current
losses = line.resistive_line_losses(current_a=1400, load_factor=0.6)
# 2.78 MWh/m

# From power — uses congested current when line is congested
losses = line.resistive_line_losses_considering_congestion(
    power_mw=550, voltage_kv=230, load_factor=0.6,
)
# 2.67 MWh/m

Corona Discharge Losses

# AC line
corona_losses = line.corona_discharge_losses(
    voltage_kv=345, load_factor=0.6, structure_config=config_ac,
)
# 0.62 MWh/m

# DC line
corona_losses_dc = line.corona_discharge_losses(
    voltage_kv=345, load_factor=0.6, structure_config=config_dc, is_hvdc=True,
)
# 0.027 MWh/m

Congestion

Congestion is the power that would need to be re-routed to alternative paths when the line cannot carry the requested load.

congestion = line.congestion(current_a=1500, voltage_kv=230)  # 1.37 MW
congestion = line.congestion(power_mw=700, voltage_kv=230)    # 14.6 MW

A result of 0 means the line can carry the load without congestion.

Overall Technical Performance

Run all calculations in a single call. The returned dictionary grows with each optional parameter provided:

# Minimum — ampacity and sag only
perf = line.overall_technical_performance(current_a=1500)
# {'ampacity_a': 1398.3, 'sag_m': 14.1}

# Add congestion (requires voltage_kv)
perf = line.overall_technical_performance(power_mw=500, voltage_kv=230)
# {'ampacity_a': ..., 'sag_m': ..., 'congestion_mw': 0}

# Add resistive losses (requires load_factor)
perf = line.overall_technical_performance(current_a=1500, load_factor=0.6)
# adds 'resistive_losses_mwh_per_m'

# Add corona (requires structure_config and voltage_kv)
perf = line.overall_technical_performance(
    current_a=1500, voltage_kv=230, load_factor=0.6,
    structure_config=config_ac,
)
# adds 'corona_inception_voltage_kv', 'corona_voltage_gradient_kv_per_cm', 'corona_losses_mwh_per_m'