Cable sizing model

Overview

The Solargis cable sizing model assists PV designers in selecting the most effective medium voltage (MV) and high voltage (HV) cables by simulating real-world technical and thermal conditions. Configuring these parameters is vital for minimizing energy transport losses and ensuring system safety. For a detailed explanation of technical terms used in this methodology, please explore our Glossary.

The model is built upon the following international standards and industry references (linked in the Further reading section):

• IEC 60287 series: Standards for calculating current ratings and active power losses.

• IEC 60502 series: Specifications for power cables with extruded insulation for rated voltages up to 30 kV.

• IEC 60038: Defined international standard voltages.

• IEC 60228: Standards for conductors of insulated cables.

• Electric Cables Handbook by G.G. Moore (BICC Cables): Used for thermal coefficients and inductive reactance calculations.

Power cable types and formations

Before calculations begin, the designer must first define the physical cable configuration within the Solargis cable sizing model from a range of XLPE-insulated options designed for ground burial:

• MV cables: These can be selected as single-core (aluminum or copper) in trefoil or flat formations, or as three-core cables that are either armored or unarmored. The rated voltages are /() = 1.8/3 (3.6) kV to 18/30 (36) kV.

• HV cables: These are specified as single-core aluminum or copper cables, arranged in either trefoil or flat formations. The rated voltages are  /() = 26/45 (52) kV to 289/500 (550) kV.

where:

• : The rated voltage between conductors for which the cable is designed.

• : The rated voltage between conductor and earth or metallic screen for which the cable is designed.

• _,:  The maximum value of the "highest system voltage'' for which the equipment may be used. More information in IEC 60038.

Figure 1: Comparison of three single-core cables in trefoil formation (left), three single-core cables in flat formation (middle), and one three-core cable (right).

Supported installation configurations

• Single-core cables (aluminum or copper) in trefoil or flat formations.

• Three-core cables (aluminum or copper), which may be armored or unarmored.

Note: Cable types are specified by the number of parallel circuits, conductor material, cross-section, insulation, voltage rating, and armoring. For example: 5 x (3 × 1c) Cu 95 mm², XLPE, 18/30(36) kV, unarmored.

Figure 2: Five parallel three-phase circuits consisting of three one-core cables in trefoil formation.

Technical criteria for cable sizing

With the cable type defined, the Solargis cable sizing model executes a series of mandatory technical checks; a cable is only considered properly sized if it passes every step in this sequence. If any criterion fails, the process must be reset by increasing the conductor cross-section or the number of parallel cables.

The technical criteria are:

• Current carrying capacity (ICCC)

• Voltage drop

• Short circuit (withstand capacity)

• Power loss

Current carrying capacity (ICCC)

The first step is to ensure the cable can handle the load. The derated capacity (), which is the capacity adapted to actual technical conditions using correction factors, must be greater than the nominal current ().

where:

• : The current carrying capacity of a power cable recalculated (adapted) to actual technical conditions (derated with correction factors).

• : The nominal current: the current flowing via cable (s) at reference conditions.

Voltage drop

Next, the system calculates the phase-to-phase voltage drop () must be less than the maximum allowed percentage voltage drop () set by the user.

where:

• : The calculated phase-to-phase voltage drop in percentage.

•  : The maximum allowed phase-to-phase voltage drop in percentage.

Short circuit (withstand capacity)

The third check verifies safety during faults. The short-circuit current rating (_,) of the cables must exceed the expected maximum thermal short-circuit current for a 1-second fault ().

where:

• : The short circuit current rating of power cable (s).

• : The expected maximum thermal short circuit current for 1sec fault.

Power loss

The final verification step ensures efficiency by checking that the calculated active power loss () caused by the nominal current is lower than the maximum power loss percentage ()  defined by the user.

where:

• : The calculated active power loss in percentage.

• : The maximum allowed active power loss in percentage.

Mathematic methods

The underlying algorithm of the Solargis cable sizing model translates these criteria into results by applying mathematical models derived from the IEC 60287 and IEC 60502 series.

Current derating and correction factors

The calculation of the actual current capacity (_,) is achieved by taking the base capacity (_,) and sequentially applying correction factors for ground temperature (_1,) , depth of laying (_2,), soil thermal resistivity (_3,), and cable proximity (_4,).

where:

• ₁: Ground temperature.

• ₂: Depth of laying.

• ₃: Soil thermal resistivity.

• ₄: Groups of circuits in proximity (thermal interaction).

Voltage drop calculation

The absolute voltage drop for parallel cables over length is calculated using the complex impedance :

where:

• : The total line-to-line voltage loss from the source to the load.

• : The one-way distance of the cable (km).

• : The AC resistance of the conductor ( ).

• : The load current (A).

• _L: Inductive reactance; The opposition to current flow caused by the magnetic field around the AC conductor.

• : The number of parallel conductors per phase. If you have two cables per phase, , which effectively halves the total impedance.

Note: This formula represents the highest voltage drop that can occur at any power factor.

Short circuit rating (Adiabatic method)

The model calculates the withstand capacity based on the conductor material, cross-section, and the duration of the fault (assumed as 1 second):

where:

• : The maximum permissible RMS thermal current (in Amperes).

• : Constant (226 for copper, 148 for aluminum).

• : Conductor cross-sectional area.

• : The length of time (in seconds) the fault persists before a breaker or fuse trips.

• : The maximum allowed temperature during a fault (e.g., for XLPE insulation).

• : The operating temperature of the cable before the fault (e.g., for XLPE ).

• : A constant related to the zero-resistance temperature of the material (for Copper, ; for Aluminum, ).

• : Accounts for the non-linear way resistance increases as the wire gets hotter during the explosion of energy.

Default acceptance criteria for voltage selection

The following tables detail the default acceptance criteria and voltage selection logic used by the model.

Note: The model automatically selects the rated voltage () based on the electrical network's nominal voltage ()  in compliance with IEC 60038.

Resistance and impedance

Calculations also involve determining DC resistance ()  and AC resistance at () , factoring in skin and proximity effects per IEC 60287-1-1. Inductance () is then derived from the conductor formation and axial spacing to complete the impedance profile.

Usage in Solargis platform

The Solargis cable sizing model is used in Energy system designer, an integrated component of the Solargis Evaluate application.

Further reading

• "Electric cables - Calculation of the current rating - Part 1-1": IEC 60287-1-1

• "Electric cables - Calculation of the current rating - Part 3-1": IEC 60287-3-1

• "Power cables with extruded insulation - Part 1": IEC 60502-1

• "Power cables with extruded insulation - Part 2" (6 kV to 30 kV)": IEC 60502-2

• "IEC standard voltages": IEC 60038

• "XLPE Land Cable System User's Guide, Rev 5": ABB

• "Electric Cables Handbook, 3rd Edition": G.G. Moore, BICC Cables