Motor Cable Selection Chart

Overview

You specify the supply and motor basis (voltage, running power factor, efficiency, starting method, starting current multiple and starting power factor, design factor, running and starting voltage-drop limits), the chart extents (motor kW range, cable size range, optional parallel-cable columns, earth conductor basis), the cable (type, formation, insulation, material), its installation and the protection data (device type, instantaneous trip multiple, fault level, clearing times, source impedance). The calculator reports:

• a maximum cable length matrix: one row per preferred motor rating (IEC 60072) with its automatically selected protective device rating \(I_N\), one column per cable size with its derated current-carrying capacity \(I_Z\), and in each cell the longest run that satisfies running voltage drop, starting voltage drop and earth-fault-loop tripping;
• a cable loading matrix giving \(I_B / I_Z\) for every pair;
• per-size short-circuit withstand, earth conductor size and earth conductor withstand checks, which do not depend on length or motor and so are reported once per column; and
• the cable data behind each column and the motor data behind each row.

Cells and column headers are colour coded:

• Grey: not applicable. Either the AS/NZS 3008 tables do not list that size for the chosen cable, the cable cannot carry the design current (\(I_B > I_Z\)), or no standard device rating covers the design current.
• Yellow: the earth-fault loop governs the length rather than voltage drop, or the size fails one of the per-size checks (short circuit, earth size, earth withstand). The length shown is still correct; the flag tells you that a larger earth, a stiffer source or a lower trip multiple would extend it, or that the size is unusable at this fault level.
• Red header: the size fails a per-size check; every cell in that column is also flagged.
• > N: the length exceeds the maximum displayed length (default 500 m), so the run is impractical and the exact figure is suppressed.

Input Parameters

Output Results

• Maximum cable length (m): rows are motor kW with the auto-selected device rating \(I_N\); columns are cable sizes with \(I_Z\); each cell is the minimum of the running voltage-drop length, the starting voltage-drop length and the earth-fault-loop length. Hovering a cell in the editor shows all three lengths and which one governs; a blank cell shows why it is not applicable. Wide charts are split every 18 size columns.
• Cable loading (%): \(I_B / I_Z\) for every available column; values above 100 % are shaded grey.
• Cable data per size: earth conductor, \(I_Z\), derating factor, \(R_c\), \(X_c\), earth \(R_e\) and \(X_e\), the Table 52 \(k\) factor, and the short-circuit, earth-size and earth-withstand results.
• Motor data per rating: full-load current \(I_{FL}\), starting current \(I_{start}\), design current \(I_B\), device rating \(I_N\) and instantaneous trip current \(I_a\).
• Summary: chart size, sizes available, usable cells, the mix of governing limits and the overall result (PASS when at least one cell is usable).
• Excel export: sheets Max Length, Loading, Cable Data, Motor Data and Inputs, with the same grey, yellow and red fills as the report.

Method

Every row starts from the motor's full-load line current and the design and starting currents derived from it:

\[ I_{FL} = \frac{P}{\sqrt{3}\,V\cos\varphi\,\eta}, \qquad I_B = I_{FL}\,k_{design}, \qquad I_{start} = k_{start}\,I_{FL} \]

The protective device is the smallest preferred rating at or above the design current, and its instantaneous trip current follows from the trip multiple of the device type:

\[ I_N = \min\{\,I_{std} : I_{std} \ge I_B\,\}, \qquad I_a = k_{mag}\,I_N \]

Preferred ratings follow AS/NZS 60898, AS/NZS 60947.2 and AS 60269. For a gM motor fuse \(k_{mag}\) defaults to 5; for an MCCB or motor circuit breaker it defaults to 10. Enter a non-zero multiplier to override either.

Every column is one cable size (or a parallel set) looked up once from the AS/NZS 3008 tables for the chosen installation: the derated capacity \(I_Z\), the operating-temperature resistance \(R_c\) and reactance \(X_c\) (Tables 34, 35 and 30), the earth conductor's \(R_e\) and \(X_e\), and the Table 52 \(k\) factor. A cell is usable when \(I_B \le I_Z\); the loading is \(I_B / I_Z\).

With the cable fixed, each length limit is linear in the run length and is solved directly:

\[ Z_{eff} = R_c\cos\varphi \pm X_c\sin\varphi, \qquad L_{run} = \frac{V_{d,max}\,V / 100}{\sqrt{3}\,I_{FL}\,Z_{eff}(\varphi)}, \qquad L_{start} = \frac{V_{d,start}\,V / 100}{\sqrt{3}\,I_{start}\,Z_{eff}(\varphi_{start})} \]

\[ L_{efl} = \frac{V_{ph}/I_a - Z_s}{|Z_c| + |Z_e|}, \qquad |Z_c| = \sqrt{R_c^2 + X_c^2}, \quad |Z_e| = \sqrt{R_e^2 + X_e^2} \]

\[ L_{max} = \min(L_{run},\; L_{start},\; L_{efl}) \]

Here \(V_{ph} = V/\sqrt{3}\) and the impedances are per kilometre, so the lengths come out in kilometres and are reported in metres. The sign in \(Z_{eff}\) follows the power factor direction (lagging adds the reactive term). The starting drop uses the starting current and the starting power factor but the same operating-temperature \(R_c\) and \(X_c\) as the running drop, which is slightly conservative because the conductor is cooler at the instant of starting. The earth-fault-loop length adds impedance magnitudes, an upper bound on the phasor sum, and uses the full phase voltage because the upstream impedance is modelled explicitly as \(Z_s\) rather than through the AS/NZS 3000 Appendix B \(0.8\,U_o\) allowance. The governing limit is the smallest of the three; ties resolve in the order running, starting, earth-fault loop.

Per-size checks. Short-circuit withstand, earth conductor size and earth conductor withstand do not depend on the run length or the motor, so they are evaluated once per column exactly as in Motor Cable Sizing: the phase conductor must withstand the prospective fault for the short-circuit clearing time, the earth must be at least the AS/NZS 3000 Table 5.1 minimum for the phase size (or the same size, by the earth basis input), and the earth must withstand the near-end earth-fault current \(V_{ph} / Z_s\) for \(t_{ef}\). A failing column keeps its lengths but is headed red and its cells are flagged.

Parallel cables. A parallel column of \(n\) cables uses \(I_Z \times n\) with no additional grouping derating, divides \(R_c\), \(X_c\), \(R_e\) and \(X_e\) by \(n\), and shares the prospective fault and the near-end earth-fault current equally between the cables (\(I_f / n\) for short-circuit withstand, \(Z_s \times n\) seen by each earth for earth withstand). These are stated assumptions: if the parallel cables run touching, apply the appropriate grouping factor to the installation inputs, and remember that unequal sharing on a fault is not covered.

Worked Examples

The 20 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_motor_cable_chart; worked examples for every calculation).

Tips & Limitations

• The report defaults to A4 landscape, and each chart matrix always prints on its own single-column page regardless of the report style's column count, so an 18-column chart stays legible. Narrow the size range or raise smallest size if you want a shorter chart.
• Use maximum displayed length to blank impractical runs: cells above it show > N instead of a number so the practical region of the chart stands out.
• Yellow cells governed by the earth-fault loop usually respond to a larger earth conductor (set the earth basis to same size as active), a lower trip multiple, or a stiffer source.
• Grey cells in the loading matrix (\(I_B > I_Z\)) are blank in the length matrix because a length is meaningless for a cable that cannot carry the load.
• A device rating is chosen from the design current only; the chart does not check the device against \(I_Z\) (AS/NZS 3000 Clause 2.5.3.1). Use Motor Cable Sizing to verify a single pair fully.
• The starting voltage-drop limit of 15 % is a common plant default, not a code requirement; set it to your specification (contactor hold-in and the driven load's torque margin usually set it).
• One installation condition per chart. Produce a separate chart for each tray, conduit or buried arrangement in the plant.
• Single-core cables with the conductors spaced, or one conductor per conduit, are rejected because AS/NZS 3008 Table 30 only tabulates trefoil and flat-touching reactance.

Developer Guide

Component: calcs/components/c0044_motor_cable_chart/ (calc type motor_cable_chart). calculations.py builds the motor rows (motor_rows, from PREFERRED_MOTOR_KW and the c0006 full-load-current formula) and the size columns (size_columns), calls the AS/NZS 3008 gateway once per base size at a 1 A reference current, runs the per-size checks with the shared check functions, and fills each cell with voltage_drop_max_length and _earth_fault_max_length from calcs/core/cable_utils.py. DEVICE_TRIP_MULTIPLIERS in the same module holds the gM and MCCB defaults. equations.py emits the two matrix report blocks (chunked at 18 size columns) and the supporting tables; excel_generator.py writes the five sheets.

Result keys: sizes (one entry per column: size, label, count, earth, availability, \(I_Z\), R/X values, \(k\), checks), rows (one per motor rating: kW, \(I_{FL}\), \(I_{start}\), \(I_B\), \(I_N\), \(I_a\)), cells[row][col] (length, loading, governing, flag, over, blank, reason and the three candidate lengths) and summary (counts of rows, sizes, available and usable cells, flagged and over-limit cells, governing mix, failing sizes).

Report engine: the chart uses the canonical matrix article block (calcs/core/reporting/blocks.py, template article_matrix, CSS classes calc-matrix, mx-blank, mx-flag, mx-over, mx-fail) and registers default_report_options of A4 landscape. Blocks carrying data-wide="1" are paginated onto their own single-column page by pagination_mixin.js.

Tests:

pytest calcs/test_c0044_motor_cable_chart.py -v

The mocked tests patch call_webcalcs_api with a synthetic per-size lookup and work one cell by hand; the live tests skip unless the 2017 rows are installed.

MCP tool: fe_calc_motor_cable_chart (calcs/mcp_adapters/motor_cable_chart.py, tests calcs/mcp_adapters/tests/test_motor_cable_chart.py) maps the fe_calc_cable_size installation vocabulary onto this component and returns the grids as max_length_m, loading_pct, governing and flagged.

Worked examples: the examples above are generated from the validation corpus (mcp_public/validation/cases/fe_calc_motor_cable_chart/) by python manage.py generate_help_examples --tool fe_calc_motor_cable_chart, which writes _motor_cable_chart_examples.html; the renderer is calcs/core/help_examples/motor_cable_chart.py. Regenerate after any table re-import or engine change; calcs/test_help_examples.py fails when the committed fragment is stale.