Three-Phase Heater Banks: Check Element Voltage Before Changing Star and Delta Connections

System boundary

A balanced sinusoidal three-phase source feeding three equal resistive heater branches. Calculations are architecture checks; they do not prescribe mains installation, establish insulation ratings or claim that a particular thick-film heater is approved for three-phase service.

Integration interfaces

Integration risks

Start with the source and the actual branch terminal map

Record the three line terminals, any neutral conductor, protective earth and every heater-branch endpoint. A heater bank may contain internal links that are not visible at its external connector. The presence of three supply wires alone does not tell you whether its resistors are connected in star or delta. Use the controlled circuit drawing and appropriate isolated verification.

Protective earth and neutral are not interchangeable names for the star point. Protective bonding has a different function from a load-current return. Do not infer the permissible connection from a photograph or another manufacturer's heater label. Qualified electrical design must establish the supply system, bonding, insulation and protective requirements for the actual equipment before any physical reconnection is considered.

In balanced star, the branch voltage is lower than line voltage

Three equal star-connected branches meet at a common point. With a balanced sinusoidal source and equal branch resistances, each branch sees line-to-line RMS voltage divided by the square root of three. Each line carries the current of its own branch. The three branch powers are equal and their sum is the total real heating power.

The square-root-of-three relationship follows from the 120-degree separation of the phase voltages, not from ordinary arithmetic division of one DC voltage among three resistors. Keep RMS voltage and current throughout this calculation. The balanced relation can apply with a floating star point under the stated symmetry, but it does not make that point a substitute for protective earth.

In balanced delta, each branch spans two lines

Each delta branch is connected between a pair of line terminals, so its RMS voltage equals the line-to-line RMS voltage. Branch current is that voltage divided by the branch resistance. The line current is the phasor difference of two branch currents and, for the balanced resistive case, its magnitude is the square root of three times branch current.

Do not add the two branch-current magnitudes arithmetically at a line terminal. Their waveforms are phase-shifted, so that sum gives the wrong RMS line current. The total real power can be checked either by summing the three branch powers or by using square root of three times line voltage times line current for this unity-power-factor balanced load.

Unchanged elements receive three times the power when moved from star to delta

Use a hypothetical low-voltage calculation with a 24-volt line-to-line RMS source and three 12-ohm branches. In star, each branch receives approximately 13.856 volts and carries 1.1547 amperes. Each dissipates 16 watts, giving 48 watts total. Line current is also 1.1547 amperes in this balanced state.

In delta on the same source, each unchanged branch receives 24 volts and carries two amperes. Each dissipates 48 watts, giving 144 watts total; line current is approximately 3.4641 amperes. The element-power increase is a factor of three, not a harmless change in wiring convention. These are analytical inputs, not rated or recommended conditions for a company product.

Equal total power requires a different resistance or supply condition

If the design objective is the same branch power on the same line voltage, the required delta branch resistance is three times the star branch resistance. In the example, 36-ohm delta branches would each dissipate 16 watts at 24 volts, matching the 12-ohm star branch power. Equal power does not mean the same element voltage or insulation exposure.

This comparison is useful when reviewing alternative bank architectures, but it is not permission to substitute elements by resistance alone. Printed geometry, terminal spacing, dielectric construction, thermal contact and the qualified control/protection arrangement still matter. An electrically equivalent total wattage can conceal a different voltage stress and a different distribution of heat within the assembly.

A floating star point moves when the branch balance is lost

The balanced voltage relationship is not generally valid for unequal branches connected to a floating star point. That point's voltage is determined by the complete three-phase network, so individual branch voltages must be solved together. A branch resistance change, an open connection or unequal switching can alter the other branches' voltages even if the source line-to-line readings remain correct.

A connected neutral changes that network constraint, while its interruption can change it again. Treat those as distinct circuit states. Do not assume the nominal balanced current predicts fault current or surviving-element stress. Model the actual source, branch connections and protective devices, and use only the approved procedures for verification; deliberately creating an energized fault is not an appropriate way to check a simple worksheet.

Keep switching mode and measurement location with the calculation

The preceding formulas describe continuous sinusoidal excitation of balanced resistors. Phase-angle firing, unequal zone duty or selective branch switching changes the waveforms and may change the balance. Use the actual controller architecture and appropriate waveform analysis rather than inserting an averaged display voltage into a continuous-supply formula.

During qualified commissioning, observe individual branch quantities where the approved measurement arrangement permits, as well as line currents and total power. Use instrumentation and isolation suitable for the circuit. A total-power reading cannot by itself establish equal branch heating, and three plausible temperature readings cannot prove the intended terminal connections. Electrical identity and thermal behavior remain separate acceptance checks.

Release the branch worksheet with the connection drawing

The handoff should show the source definition, selected links, neutral treatment, branch resistance range and calculated element voltage/current/power. Include relevant cold and operating resistance states and the source's real limiting behavior. Identify which connections are fixed and which, if any, are allowed to be changed under a controlled service procedure.

Before accepting a star/delta alternative, reconcile those electrical results with element limits, thermal distribution, sensing and independent protection. Preserve the approved drawing and verify it after maintenance. The practical outcome is that every printed heater branch receives the voltage and power actually reviewed for it, rather than inheriting an unsupported assumption from the bank's total wattage or supply label.