Transmission Line Capacity and Cost Calculator – Explanatory Notes#

Objective#

In many developing-country projects, we do not have detailed engineering data about existing or planned transmission lines.
The idea is to build a very simplified tool that can still provide a reasonable order of magnitude for:

  • the transfer capacity of a transmission line (MW), and

  • the investment cost of constructing such a line (MUSD).

This tool is meant for pre-feasibility or planning purposes when limited information is available.
Even approximate results are valuable to compare options or identify bottlenecks.

1. Basic User Inputs#

Only three inputs are required:

  1. Number of circuits (N_circ)

    • A circuit is one complete three-phase system (three conductors).

    • N_circ = 1 → single-circuit line.

    • N_circ = 2 → double-circuit line (higher capacity and reliability).

  2. Voltage (V_kV)

    • Choose among 220, 330, 400, or 500 kV.

    • Determines the technical parameters and unit costs used by the tool.

  3. Line length (L_km)

    • Approximate distance between substations, in kilometers.

    • Can be estimated quickly using Google Maps or GIS tools.

Optional settings:

  • N-1 criterion (TRUE/FALSE)

    • If TRUE, the line must still transmit power when one circuit is lost.

    • A single-circuit line cannot satisfy N-1.

  • Terrain factor

    • Multiplier to reflect construction difficulty:
      1.0 = normal terrain, 1.2 = difficult, 1.5 = mountainous.

2. Understanding Transmission Line Capacity#

The capacity of a transmission line (how much power it can carry) is not unlimited.
It is typically constrained by three main physical limits:

  1. Thermal limit – how much current the conductor can carry before overheating.

  2. Stability limit – how much real power can flow before the sending and receiving systems lose synchronism (angle stability).

  3. Voltage limit – how far voltage can be maintained along the line before it collapses due to reactive power imbalance.

Consequently:

  • For short or medium lines (< 200 km), the capacity is usually limited by thermal heating of conductors.

  • For longer lines (200–400 km), stability (angle or voltage) starts to limit transfer.

  • Beyond 400–500 km, voltage control or compensation becomes essential.

3. Step 1: Surge Impedance Loading (SIL)#

SIL is a theoretical value representing the natural power level at which the line neither generates nor consumes reactive power.
It depends on the surge impedance (Zc) of the line.

\[ SIL = \frac{V_{kV}^2}{Z_c} \]

  • Zc (surge impedance) is a property of the line determined by its geometry and conductor configuration.
    For most high-voltage AC overhead lines, Zc ≈ 300 Ω is a reasonable average.

  • Example: for a 400 kV line, SIL ≈ (400² / 300) ≈ 533 MW per circuit.

SIL gives the base scale for how much power a line can carry under ideal conditions.
Actual usable power will be below this due to stability and thermal limits.

4. Step 2: Stability Limit (\(P_{stab}\))#

As distance increases, the line reactance increases, and the angle between sending and receiving ends becomes harder to control.
This defines the stability limit.

We approximate this by applying a derating factor K(L) that decreases with line length:

\[ K(L) = \frac{1}{1 + \frac{L_{km}}{L_0}} \]

where:

  • L0 = “stability length” from the parameter table (e.g., 400 km for 220 kV, 250 km for 400 kV).

Then:

\[ P_{\text{stab}} = SIL \times K(L) \times N_{\text{circ}} \]

  • For short lines, K(L) ≈ 1 → almost full SIL available.

  • For long lines, K(L) < 1 → stability significantly reduces power transfer.

This is a simplified way to represent both angle and voltage stability effects.

5. Step 3: Thermal Limit (P_thermal)#

The thermal limit corresponds to conductor heating due to electric current.

\[ P_{\text{thermal,circ}} = \frac{\sqrt{3} \times V_{kV} \times I_{\text{th,circ}}}{1000} \]

where:

  • I_th,circ = rated current per circuit (from the voltage table).

Examples:

  • 220 kV line at 1500 A → 572 MW per circuit.

  • 400 kV line at 900 A → 624 MW per circuit.

  • 500 kV line at 2000 A → 1730 MW per circuit.

If there are multiple circuits:

\[ P_{\text{thermal,total}} = N_{\text{circ}} \times P_{\text{thermal,circ}} \]

If N-1 is enforced:

\[ P_{\text{thermal,N-1}} = (N_{\text{circ}} - 1) \times P_{\text{thermal,circ}} \]

Then the limit used is:

  • If N-1 = TRUE → use \(P_{\text{thermal,N-1}}\)

  • If N-1 = FALSE → use \(P_{\text{thermal,total}}\)

6. Step 4: Voltage Stability (P_voltage)#

For simplicity, the voltage limit is expressed as a multiplier of SIL:

\[ P_{\text{voltage}} = \beta \times SIL \times N_{\text{circ}} \]

where β is a simple factor:

  • β = 1.0 for normal, uncompensated lines,

  • β = 1.5–2.0 for strong or compensated systems.

This term can be ignored if the stability limit is already applied through K(L).

7. Step 5: Available Transfer Capacity#

Finally, the model takes the lowest of all relevant limits:

\[ P_{\text{avail}} = \min(P_{\text{stab}}, P_{\text{thermal,limit}}, P_{\text{voltage}}) \]

This is the estimated usable transfer capacity in MW under the assumed conditions.

8. Step 6: Cost Estimation#

8.1 Overhead Line Cost#

\[ C_{\text{line}} = L_{km} \times N_{\text{circ}} \times C_{\text{unit,km}} \times \text{Terrain factor} \]

  • C_unit,km = cost per km per circuit from the parameter table (MUSD/km).

  • Includes towers, foundations, conductors, insulators, and installation.

Typical values:

  • 220 kV: 0.35 MUSD/km

  • 330 kV: 0.45 MUSD/km

  • 400 kV: 0.50 MUSD/km

  • 500 kV: 0.80 MUSD/km

These are average turnkey costs excluding substations and contingencies.

8.2 Substation Cost#

\[ C_{\text{sub}} = N_{\text{sub}} \times C_{\text{unit,sub}} \]

Usually two terminal substations (sending and receiving ends).
Typical costs:

  • 4–10 MUSD per 220–500 kV substation, depending on voltage and configuration.

8.3 Reactive Power Compensation#

If applicable (for very long lines > 400 km):

\[ C_{\text{comp}} = N_{\text{comp}} \times C_{\text{unit,comp}} \]

Typical compensation equipment:

  • SVC, STATCOM, or series capacitors

  • 3–6 MUSD for 220–330 kV, 6–10 MUSD for 400–500 kV.

8.4 Total Investment Cost#

\[ C_{\text{total}} = C_{\text{line}} + C_{\text{sub}} + C_{\text{comp}} \]

Optional: $\( \text{Cost per MW} = \frac{C_{\text{total}}}{P_{\text{avail}}} \)$

9. Interpreting the Results#

The model outputs:

  • Available capacity (MW): a rough estimate of how much power the line can carry considering physical limits and reliability.

  • Total cost (MUSD): an approximate investment cost including line, substations, and optional compensation.

For short lines, the thermal limit usually binds (capacity increases with voltage and conductor size).
For longer lines, stability constraints reduce the effective capacity even if conductors could carry more current.

These outputs should be seen as order-of-magnitude indicators — useful for comparing corridors, voltage choices, or reliability scenarios before more detailed engineering data becomes available.